Hygrometry

228. If the temperature of air is 16.5 0C and dew point is 6.5 0C , find the relative humidity of air. ( SVP at 6, 7 , 16 and 17 0C are 7.05, 7.51, 13.62 and 14.42 mm of Hg respectively ) [ 51.9%]
229. What is the dew point on a day if the humidity is 40% on that day when the temperature is 300 C.
[12 0C ]
230. On a certain day the dew point is 8.5 0C and the room temperature is 18.4 0C. Find the RH if the maximum vapour pressure for 8, 9, 18 and 19 0C are 8.04, 8.61, 15.46 and 16.46 mm of Hg respectively. [ 52.5 %]

Transfer of heat
231. A man, the surface area of whose skin is 2 m2, is sitting in a room where the air temperature is 20 0C. If the temperature of skin is 28 0C , find the rate at which his body loses heat. The emissivity of his skin is 0.97 and  = 5.7 x 10-8 W/m2 K4. [ 92.2 W]
Hints: The rate of heat loss due to radiation according to Stephen’s law is given by , where is emissivity.
232. Calculate the rate of loss of heat from an unclothed person standing in air at 23 0C . Assuming that the skin temperature is 34 0C and the body surface area is 1.5 m2 , emissivity = 0.7 and  = 5.7 x 10-8 W/m2 K4. [ 46.85 W]
Hints: The rate of heat loss due to radiation according to Stephen’s law is given by .
233. A closed metal vessel contains water (i) at 30 0C (ii) at 75 0C . The vessel has surface area 0.5 m2 and a uniform thickness of 4 mm. If the outside temperature is 15 0C , calculate the heat loss per minute by conduction in each case. ( Thermal conductivity of metal = 400 W / mK ) [ 4.5×107, 18 x107J]
Hints: Use the relation of rate of flow of heat due to conduction is

234. Assuming that the thermal conductivity of woolen glove is equivalent to a layer of quiescent air 3 mm thick, determine the heat lost per minute from the man’s hand of surface area 200 cm2 0n a winter’s day when atmospheric temperature is 3 0C. The skin temperature is taken 34 0C and thermal conductivity of air is 24 x 10-3 W/mK. [ 354 J/min]
Hints: Use the relation of rate of flow of heat due to conduction is

235. A bar of 0.2 m in length and cross-sectional area 2.5 x 10-4 m2 is ideally lagged. One end is maintained at 373 k and other is kept in melting ice. Calculate the rate at which ice melts. [ 1.47 x 10-4 Kg / s ]
Hints: At first calculate and the energy is used to melt ice. So, mL = Q.

236. One face of a sheet of cork is 3 mm thick is placed contact with one face of the of a sheet of glass 5 mm thick, both sheet being 20 cm square. The outer faces of this square composite sheet are maintained at 100 0C and 20 0C , the glass being at the higher temperature. Find (a) the temperature of the glass – cork interface, (b) the rate at which heat is conducted across the sheet, neglecting edge effect. Thermal conductivity of cork and glass are 6.3 x 10-2 W/mK and 7.2 x 10-1 W/mK respectively. [ 90 0C, 57.6 W ]
Hints: The rate of flow of heat through glass due to conduction, ………..(i) Similarly, rate of flow of heat through cork
………..(ii)
Rate of flow of heat through glass is equal to that of cork. So, equating (i) and (ii),  can be determined.
237. Estimate the rate of heat loss from a room through glass window of area 2 m2 and thickness 3 mm when temperature of room is 20 0C and that of air outside is 5 0C. Thermal conductivity of glass is 0.72 W/mK respectively. [ 7200 W]
Hints: Use the relation of rate of flow of heat due to conduction

238. The silica cylinder of a radiant wall heater is 0.6 m long and has a radius of 5 mm. If it is rated at 1.5 kW, estimate the temperature when operated. State two assumptions you have made in making your statement. Given Stephen constant is 6 x 10-8 W/m2K4. [1070 K]
Hints: Use relation . The assumptions are (a) The heater is considered as a perfectly black body, (b) The temperature of surrounding is considered to absolute zero.

239. What is the ratio of the energy per second radiated by the filament of a lamp at 2500 K to that radiated at 2000 K, assuming the filament is a black body radiator. The filament of a lamp can be considered as a 90% black body radiator. Calculated the energy per second radiated when its temperature is 2000 K and surface area is 10-6 m2. [ 2.44, 0.82] Hints: Apply relation for both lamps and divide them to get result. In second case, take efficiency 90 % or 0.9.
240. The sun is a black body of surface temperature 6000 K. If the sun’s radius is 7 x 108 m, calculate the energy per second radiated from its surface. The earth is about 1.5 x 1011 m from the sun. Assuming all the radiation from the sun falls on a sphere of this radius, estimate the energy per second per meter square ( solar constant ) received by the earth. Stephen constant is 5.7 x 10-8 W/m2K4. [ 1600 W/m2 ] Hints: Apply relation to obtain energy radiated by sun per second. The energy radiated by sun spherically distributes all over and solar constant is the energy received by earth per unit area per unit time. So divide the power radiated by sun ‘P’ by surface are of the sphere made by the radius 1.5 x 1011m. i.e Solar constant S =
241. A sphere of radius 2 cm with a black surface is cooled and then suspended in a large evacuated enclosure the black walls of which are maintained at 27 0C. If the rate of change of thermal energy of the sphere is 1.85 J/s, when its temperature is -73 0C, calculate the value for the Stephen constant. [5.7 x 10-8 W/m2K4 ]
Hints: The rate of heat loss by black body is given by .

242. The element of an electric fire, with an output of 1.0 kW, is a cylinder 25 cm long and 1.5 cm in diameter. Calculate the temperature when in use of it behaves as a black body. [ 1105 K ]
Hints: Use relation , where A is the curved surface area of cylindrical electric element, equal to 2 r h
243. A solid copper sphere of diameter 10 mm is cooled to a temperature of 150 K and is then placed in an enclosure maintained at 290 K. Assuming that all interchange of heat is by radiation, calculate the initial rate of rise of temperature of the sphere. The sphere may be treated as a black body. Density of copper 893 kg /m3, specific heat capacity of copper 3.7 x 102 J / kgK and Stephen constant 5.7 x 10-8 W/m2K4. [ 0.068 K/s]
Hints: Use relation . This energy is used to increase the temperature. So, . Equate the relations to obtain .
244. The element of 1 kW electric fire has a surface area of 0.006 m2. Estimate the working temperature. Stephen constant is 5.7 x 10-8 W/m2K4 [ 1300 K]
Hints: Use relation .
245. A roof measures 20m x 50m and is blackened. If temperature of the sun’s surface is 6000 K and its radius is 7.8 x 108 m, and the distance from the earth is 1.5 x 1011 m calculate how much solar energy is incident on the roof per minute. Assume that the half of the energy is lost in passing through the earth’s atmosphere and the roof is normal to the sun’s rays. [ 5.6 x 107 J]
Hints: Power radiated by sun and solar constant S = . The additional term ½ is taken according to question that half of the energy is lost in passing through the earth’s atmosphere. Finally multiply area of the roof with solar constant.
246. Calculate the apparent temperature of the sun from the following data. Sun’s radius = 7.04 x 105 Km. Distance from earth = 14.72 x 107 Km Solar constant = 1400 w m-2 Stephen constant = 5.7 x 10-8 W m-2 k-4 [ 5450 0C ]
Hints: Total power released by sun is P = S × 4 r2, where ‘r’ is the distance of sun from earth. Finally use the Stephen’s law , where A be the surface area of sun, given by A = 4 R2.

Thermodynamics

247. For hydrogen, the molar heat capacity at constant volume and pressure are respectively 20.5 J/molK and 28.8 J/molK. (a) Which heat capacity is related to internal energy ? (b) Calculate the molar gas constant. (c) Calculate the heat needed to rise the temperature of 8g hydrogen from
100 C to 150 C at constant pressure? (d) Increase in the internal energy of the gas. (e) External work done.
[ 8.3 J/molK, 576 J, 410 J, 166 J] Hints: (a) Specific heat capacity at constant volume Cv is related to the internal energy. (b) Molar gas constant R = Cp – Cv (c) dQ = N  Cp  dT, where N is the number of mole = 4/2 = 4. (d) Increase in internal energy dU = N  Cv  dT (e) External work done dW = dQ – dU
248. A gas has a volume of 0.02 m3 at pressure of 2 x 105 Pa and temperature of 27 0C. It is heated at constant pressure until its volume be 0.03 m3. Calculate the (a) External work done, (b) The new temperature of the gas, (c) Increase in internal energy of the gas. Mass of the gas is 16 g, molar heat capacity at constant volume is 0.8 J/molK and its molar mass is 32 g. [ 2000J, 450K, 60J] Hints: (a) External work done dW = P  V (b) Ideal gas equation (c) Increase in internal energy dU = N  Cv  dT
249. If ratio of the principal specific heat capacities of a gas is 1.4 and its density at stp is 0.090 kg/m3. Calculate the specific heat capacities at constant pressure and at constant volume. [ 144 x104, 1.03 x 104 J/kgK] Hints: Pressure exerted by gas P =  r T. So, gas constant r = Now, cp – cv = r …………(i) and cp = 1.4 cv ………..(ii) Solving equation (i) and (ii), cp and cv can be determined.
250. Given that the volume of a gas at stp is 2.24 x 10-2 m3 /mol , calculate the molar gas constant R and use it to find the difference between the quantities of heat required to raise the temperature of 0.01 kg of oxygen from 0 0C to 10 0C when (a) pressure (b) volume of the gas is kept constant. Given relative molecular mass of the oxygen = 32. [ 8.3 J/molK, 25.9 J] Hints: Molar gas equation PV = NRT gives the molar gas constant ‘R’. Energy required to heat at constant pressure dQ = N Cp  T …………..(i) Energy required to heat at constant volume dU = N Cv  T ……………..(ii) Subtracting, the obtained result is dQ – dU = N  T  ( Cp – Cv) = N  T  R.
251. An ideal gas at a temperature of 290 K and a pressure of 1.0 x 105 N/m2, occupies the volume of 1.0 x 10-3 m3. Its density under these conditions is 0.30 kg/m3. It expands at a constant pressure to a volume of 1.5 x 10-3 m3.Calculate the energy added. It is now compressed isothermally to its original volume. Calculate its final pressure and temperature and the difference between its initial and final internal energy. Given Cv = 7.1 x 102 J / Kg K . [ 81J, 1.5 x 105 N/m2, 435K, 30.9 J] Hints: Ideal gas equation gives the final temperature T2. Pressure exerted by gas P =  r T. So, gas constant r = . Also, specific heat capacity at constant pressure cp = cv + r and Heat energy added dQ = m  cp  T Again, Ideal gas equation P2V2 = P3V3 gives the final pressure P3. Difference between initial and final internal energy is dU = m x cv x dT
252. The density of ideal gas is 1.6 kg/m3 at 27 0C and 1.00 x 105 N/m2 pressure and specific heat capacity at constant volume is 312 J/ kgK. Find the ratio of specific heat capacities at constant pressure and constant volume. [1.67] Hints: Pressure exerted by gas P =  r T. So, gas constant r = . Now, specific heat capacity at constant pressure cp = cv + r. And, ratio of specific heat capacities  = cp / cv
253. A gas in a cylinder of temperature 17 0C and a pressure of 1.01 x 105 N/m2 is to be compressed to one-eighth of its volume. What would be the difference between the final pressures if the compression is done (a) isothermally, (b) adiabatically ? (c) What would be the final pressure in the later case? Given  = 1.40 [10 .48 x 105 N/m2, 666 K] Hints: When gas is compressed isothermally, P1 V1 = P2 V2 When gas is compressed adiabatically, P1 V1 = P2 V2
254. A liter of air initially at 20 0C and 760 mm of Hg is heated at constant pressure until its volume is doubled. Find (a) its final temperature, (b) external work done, (c) the quantity of heat supplied. Given density of air at stp is 1.293 kg/m3 and Cv = 714 J/kgK. [ 586 K, 101.2 J, 355J] Hints: (a) Ideal gas equation gives final temperature (b) External work done, W = P V, where V = 2 lit – 1 lit = 1 lit = 10-3 m3 (c) Volume of gas at 00C is given by Or, Or, V1 = 9.32 x 10-4 m3 Therefore , mass of the gas m =  x V = 1.293 x 9.32 x 10-4 = 1.205 x 10-3 kg Quantity of heat supplied dQ = dU + dW = m x cv x dT + P V
255. A mass of air occupying initially a volume 2 x 10-3 m3 at a pressure 760 mm of Hg and temperature 20 0C is expanded adiabatically reversibly to twice its volume, and then compressed isothermally and reversibly to a volume of 3 x 10-3 m3. Find the final temperature and pressure. Given  = 1.40
[ 222K, 384 mm of Hg] Hints: Expression for adiabatic expansion P1 V1 = P2 V2 Expression for isothermal compression P2 V2 = P3 V3. Where, P3 is the final pressure. Similarly, the expression for adiabatic expansion T1V1-1 = T2V2-1. In isothermal process, temperature remains constant. So, T2 is the final temperature after isothermal compression.
256. A petrol engines consumes 5 kg petrol per hour. If the power of the engine is 20 KW and the calorific value of petrol is 11 x 103 K Cal per kg, calculate the efficiency of the engine. [ 31.15%] Hints: Efficiency of an engine Where, output = 20 KW = 20000 W Input = 5 Kg petrol per hour = 5 / 60 x 60 kg per sec. = Watt
257. An ideal heat engine operates in a Carnot Cycle between 227 0C and 127 0C. It absorbs 6 x 104 J at the higher temperature . How much work per cycle is this engine capable of performing? [ 5 x 104 J ] Hints: Efficiency of an engine = So, = Where, T2 = temperature of sink in absolute scale T1 = temperature of source in absolute scale Input = 6 x 104 J
258. A Carnot engine operates between a hot reservoir at 320 K and a cold reservoir 260 K. If it absorbs 500 J of heat from hot reservoir, how much work does it deliver? If the same engine working in reverses as a refrigerator, how much work must be supplied to remove 1000 J of heat from the cold reservoir? [ 4333 J] Hints: Efficiency of a heat engine is , = where, T2 = temperature of sink, 260 K T1 = temperature of source, 320 K Input = 500 J Output = ? If the same engine works as a refrigerator, its efficiency Where,  = efficiency obtained from above , 18.75 % Q2 = heat taken from cold body, 1000 J W = work supplied, to determine.
259. A motor in a refrigerator has a power of output 200 W. If the freezing compartment is at 270 K and room temperature is 300 K, assuming ideal efficiency, what is the maximum amount of heat that can be extracted from the freezing compartment in 10 min? [ 1.1 x 106 ]

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Temperature

189. At what temperature degree Fahrenheit scale shows twice the reading of degree centigrade? [ 160 0C] Hints: The relation between C and F scale of temperature is . Take C = , then F = 2.
190. At what temperature degree Fahrenheit scale shows half of the reading of degree centigrade? [ – 24.62 0C] Hints: Take C = , then F will be /2 and put the value in relation
191. At what temperature Fahrenheit and Kelvin scale give the same reading?
[ 574.25K]
Hints: Take the temperature F = , then K is also  and put the value in relation
192. The normal temperature of human body is 37 0C. What is its value in 0F and Kelvin scale? [ 98.60F, 310 K]
193. A faulty thermometer has its fixed points –100C and 130 0C. This thermometer reads the temperature of an object 60 0C. Find the correct temperature of the body in Celsius scale. [ 500 C ] Hints: The term where L is lower fix point and U is upper fix point, remains constant for all scale of thermometer. Use same expression for both correct thermometer and faulty thermometer.
194. A faulty Celsius thermometer reads – 4 0C when placed in melting ice and reads 98 0C when placed in the contact with steam at normal pressure. What the correct temperature in that scale when it reads room temperature 32 0C ? [ 35.3 0C ]

Thermal Expansion
195. A steel meter scale has length 100.00 cm at temperature 10 0C. If the temperature rises to 20 0C, what is the length of the scale? (  for steel 1.6 x 10-6 / k). If a road of length 1 km is measured at 20 0C, what will be the error in the measurement? Hints: The length of the scale at temperature 20 0C is given by l2 = l1 [ 1+ (2 – 1)]. Divide length of the road by the length of the scale at 20 0C to obtain its reading.
196. An aluminum rod when measured with a steel scale, both being at 25 0C appears to be 1 m long. If the scale is correct at 0 0C, (a) what is the true length of the scale at that temperature? (b) What will be the length of the rod at 0 0C? Linear expansivity of aluminum is 26 x 20-6 /K and of steel is 12 x 10-6/K. [1.0003m, 99.96m] Hints:
197. A glass vessel of volume 200 cm3 is just filled with mercury at 100C. If the temperature raised to 120 0C, how much mercury overflow? ( for glass 1.2 x 10-6 / k and  for mercury 1.6 x 10 –4 /k ) [ 3.44 cm3] Hints: The overflowing mercury is the difference between the volume of mercury and the volume of vessel at 120 0C. So, determine volume of mercury and volume of vessel at 120 0C separately and calculate the difference between them.
198. A thermal tap used in certain apparatus consists a silica rod which fits tightly inside an Aluminum tube whose internal diameter is 8 mm at 00 C. When temperature is raised, the fit is no longer exact. Calculate what change of temperature is necessary to provide a channel whose cross-section is equal to that of a tube of 1mm internal diameter. Linear expansivity of Si and Al are 8 x 10-6/K and 26 x 10-6 /K. [ 434 K ]
Hints: Let at temperature , the channel area will be equal to the cross section area of a tube of 1 mm internal diameter which is given by . The channel area is equal to the difference between the cross-section areas of the cylinder(Al) to piston(Si). So, (A)Al – (A)Si = .

199. A brass pendulum clock gives correct time at 15 0C. How many second does it lose or gain per day when the temperature changes to 20 0C? ( for brass 0.000019 / k ) [ 4 s ]
Hints: Time period of pendulum at 15 0C is and that of 20 0C is . Since correct time of pendulum is 2 second, put T1 = 2 second. The relation between l2 and l1 is . Put the value of l2 and divide T1 to T2. Determine difference between T1 and T2 and finally determine gain or lose in time per day.
200. A steel wire 8m long and 4 mm in diameter is fixed to two rigid support. Calculate the increase in tension when the temperature falls by 100 C? Given linear expansivity of steel 12 x 10-6 /K, Young modulus for steel 2 x 1011 N/m2 . [ 300 N ]
Hints: Young’s modulus Y = , where F is force or tension, l is initial length, A is cross section area and e is extension or contraction of the wire. Use relation or Or, e = where e = is the contraction. Finally use the relation of young’s modulus to calculate tension.
201. A steel cylinder has an Aluminum piston and at temperature of 200 C, internal diameter of cylinder is exactly 10 cm, there is an around clearance of 0.05 mm between the piston and the cylinder wall. At what temperature will the fit be perfect? Given linear expansivity of steel and Aluminum are 1.2 x 10-5 /K and 1.6 x 10-5 /K respectively. [ 2700 C ]
Hints: To fit perfectly, the diameter of steel piston should be exactly equal to the diameter of aluminum cylinder. Consider the temperature  at which their diameters are exactly equal. So, .

202. Aniline is a liquid which doesn’t mix with water and when a small quantity of it is poured into beaker of water at 200 C, it sinks to the bottom, the densities of two liquids at 200 C are 1021 and 998 Kg/m3 respectively. At what temperature must the beaker and its contents be heated so that the aniline will form a globule which just floats in the water? Given absolute expansivity of aniline and water are 0.00085 /K and 0.00045 /K respectively. [ 790 C ]
Hints: To satisfy the mentioned condition, density of aniline must be equal to the density of water. So, let at temperature , their densities are exactly equal i.e. .

203. A certain Fortin barometer has its pointer, body and scale made from brass. When it is at 00 C, it records pressure 760 mmHg. What will it read when its temperature is increased to 200C if pressure of the atmospheric remains unchanged? Given cubical expansivity of mercury 1.8 x 10-4 /K, Linear expansivity of brass 2 x 10-5 /K. [ 762.4 mm Hg ] Hints: Use the expression of correction of barometer.
204. Using the following data, determine the temperature at which wood will just sink in benzene? Density of benzene at 00C = 900 kg / m3. Density of wood at 00C = 880 kg / m3. Cubical expansivity of benzene = 0.0012 / k
Cubical expansivity of wood = 0.0015 / k
Hints: To satisfy the mentioned condition, density of wood should be exactly equal to the density of the benzene. So, let at temperature , their densities are exactly equal i.e.
Calorimetry / Change of state
205. A steel ball of mass 80 gram is taken from a furnace of temperature 2000C and dropped in a copper calorimeter of mass 50 gram containing 65 gm of water at temperature 20 0C. If the final temperature of the mixture rises to 22.5 0C, calculate the specific heat capacity of the steel. ( Specific heat capacity of copper is 0.1 cal / gm k. Hints: In the above phenomenon, steel ball loss heat but calorimeter and water gains heat. According to principle of calorimetry, heat loss is equal to the heat gain. So, heat loss by steel ball Q1 = m  S   Heat gain by caloriemeter and water Q2 = (m  S  ) for water + (m  S   ) for calorimeter. From principle of calorimetry, Q1 = Q2
206. A copper ball of mass 15 g is held in a flame until it has acquired the temperature of the flame. It is then quickly transferred to a copper calorimeter of mass 66 g containing 50 g of water at 20 0C. If the final steady temperature of the mixture is 27.5 0C, calculate the temperature of the flame. [323 0C]
207. Two identical calorimeters each of heat capacity 12 J/K, one contains 8 x 10-5 m3 of water and takes 150 second to cool from 325 K to 320 K, and the other contains an equal volume of an unknown liquid which takes 50 second to cool over the same range of temperature. If the density of the liquid is 800 kg/m3, what is the specific heat capacity of liquid over the temperature range? Given , density of water 1000 kg/m3 and heat capacity 4200 J/K. [ 1625 L/kgK]
208. A lead bullet moving with velocity of 400m/s strikes a target and is brought to rest. If half of the kinetic energy goes to raise the temperature of the bullet, by how many degrees will its temperature rise? Given specific heat capacity of the bullet is 0.13 J/g 0C . [ 307.20C] Hints: According to question, half of the KE changes into heat. So, ( ½ mv2 ) = m x s x 
209. A substance takes 3 min in cooling from 50 0C to 45 0C and takes 5 min in cooling from 45 0C to 40 0C. What is the temperature of its surrounding? How much time will it take to cool from 40 0C to 35 0C ? [ 35 0C, 15 min ]
210. How much energy is required to convert 500 g ice of temperature –5 0C to steam of temperature 100 0C ? ( Specific and latent heat of ice are 0.5 cal /gm 0C and 80 cal /gm and latent heat of steam is 340 cal / gm. )
211. 5 gm of ice at 0 0C is dropped into a beaker containing 20 g of water at 40 0C. What will be the final temperature? [ 16 0C ]
212. What is the result of mixture when 400g of water and 100 g of ice at 00C are in a copper calorimeter of mass 500g and 100 g of steam is passed into it? [
213. What is the result of mixing 20g of ice at -10 0C and 50g of water at 300C ? [ Specific heat of ice 2100 J/kg K & latent heat of ice 3.34 x 105 J/kg ]
214. 1 g of steam at 100 0C can melt how much ice at 0 0C ? [ 8 g ]
Ideal Gas Equation
215. A container of gas has volume 0.1 m3 at a pressure of 2 x 105 N/m2 and a temperature of 27 0C. (a) Find the new pressure if the gas is heated at constant volume to 87 0C, (b) The gas pressure is now reduced to 1.0 x 105 N/m2 at constant temperature. What is the new volume of the gas? (c) The gas cooled to – 73 0C at constant pressure. Find the new volume of the gas. [2.4 x 105 N/m2, 0.24 m3, 0.13 m3 ]
216. A cylinder of gas has mass of 10.0 kg and pressure of 8.0 atmosphere at 27 0C. When some gas is used in a cooled room at – 3 0C, the gas remaining in the cylinder at this temperature has a pressure 6.4 atm. Calculate the mass of the gas used. [ 1.1 kg ] Hints: From ideal gas equation, P1V = m1 r T1 ………..(i) When some gas is used in a cool room, the equation for the remaining gas will be P2V = m2 r T2 ………..(ii) Dividing equation (i) by (ii),
217. Two glass bulb of equal volume are joined by a narrow tube and are filled with a gas at stp. When one bulb is kept in melting ice and the other is placed in hot bath, the new pressure is 877.6 mm of Hg. Calculate the temperature of the bath. [ 100 0C ] Hints: When both bulbs are in STP, the ideal gas equation will be P1 (2V) = m r T1 So, m = When one bulb is placed in melting ice, P1 V = m1 r T1 So, m1 = When another bulb is placed in hot bath, mass of gas in the bulb is m2 = Since mass of gas remains constant, m1 + m2 = m
218. Two vessels of capacity 1.00 litre are connected by a tube of negligible volume. Together, they contain 3.42 x 10-4 kg of helium at a pressure of 800 mm of mercury at temperature 27 0C. Calculate (a) value for the constant ‘r’ for helium, (b) the pressure developed in the apparatus if one vessel is cooled to 0 0C and next is heated to 100 0C. [ 2080 J/kg K, 842 mm ]
Hints: Both bulbs are in same pressure, the ideal gas equation will be P (2V) = m r T where, pressure P = 800 mm of Hg = 800 x 13600×9.8 Nm2 volume V = 1 litre = 10-3 m3 mass m = 3.42 x 10-4 Kg temperature T = 270C = 300 K
219. What volume of liquid oxygen( density 1140 kg/m3) may be made by liquefying completely the contents of a cylinder of gaseous oxygen containing 100 litre at 120 atm pressure at 20 0C? Assume that oxygen behaves as an ideal gas in this latter region of pressure and temperature. Given 1 atmosphere = 1.01 x 105 N/m2, molar gas constant is 8.31 J /molK and relative molecular mass of oxygen is 32. [ 0.014 m3 ]
220. A sealed bottle full of water is placed in a strong container full of air at standard atmospheric pressure and at a temperature of 10 0C. The temperature in the container is raised to and maintained at 100 0C. Neglecting the expansion of the bottle and the container, what is the new pressure in the container? If the bottle breaks, what will be the pressure be? [ 1.3 x 105 N/m2, 2.3 x 105]
221. A container of gas has a volume of 0. 1 m3 at pressure of 2 x 105 N / m2 and temperature 27 0C. (i) Find the new pressure if the gas is heated at constant volume to 87 0C. (ii) The pressure is now reduced to 1 atmosphere at constant temperature.
Kinetic theory of gas
222. Calculate the root – mean- square speed at 0 0C of (i) Hydrogen molecules and (ii) Oxygen molecules, assuming 1 mole of the gas occupies a volume of 2 x 10-2 m3 at 0 0C and pressure 105 N/m2. Relative molecular masses of hydrogen and oxygen are 2 and 32 respectively. [1732 m/s, 433 m/s]
Hints: The pressure exerted by gas in terms of root mean square speed is given by . Replace density by mass per unit volume and finally determine C.
223. Assuming helium molecules have a root mean square speed of 900 m/s at 27 0C and 105 pressure, calculate the rms speed at (i) 127 0C and 105 N/m2, (ii) 27 0C and 2 x 105 N/m2 pressure. [ 1039 m/s, 900 m/s]
Hints:

224. Air may be taken to consist of 80 % nitrogen molecules and 20 %oxygen molecules of relative molecular masses 28 and 32 respectively. Calculate (a) ratio of the rms speed of nitrogen molecules to that of oxygen molecules, (b) ratio of the partial pressure of nitrogen and oxygen molecules, (c) ratio of the rms speed of nitrogen molecules at 100C to that at 2000C. [ 1.07:1, 4:1, 0.87:1]
225. Calculate the pressure in mm of Hg exerted by Hydrogen gas if the number of molecules per cm3 is 6.80 x 1015 and the root mean square speed of the molecules is 1.90 x 103 m/s. Given Avogadro constant is 6.02 x 1023 and relative molecular mass of hydrogen is 2.02. [ 0.21 mm of Hg ]
226. Assuming that the density of Nitrogen at stp to be 1.251 kg /m3 find the root mean square velocity of nitrogen molecules at 127 0C. [ 597 m/s ]
Hints: At first determine rms speed of nitrogen at stp and then determine its value at another temperature by using relation .
227. Air at 273 K and 1.01 x 105 N/m2 pressure contains 2.7 x 1025 molecules per cubic meter. How many molecules per cubic meter will there be at a place where temperature is 223 K and pressure is 1.33 x 104 N / m2

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Revision for ambitious students

132. A body moving through air at high speed ‘v’ experiences a retarding force given by f = k A  vx, where A is the surface area of the body,  is density of air and k is dimensionless constant. Deduce the expression.
133. The position of a particle moving along on X – axis is given by x = A t2 + Bt + C. The numerical value of A, B and C are 1, -4, 2. Find (i) dimension of A, B and C, (ii) the velocity of the particle at t = 4 sec, (iii) acceleration of the particle when t = 4 sec, (iv) the average velocity during the interval t = 0 to t = 5 sec.
134. A stone is dropped from a balloon going up with a velocity 5 m / s. If the balloon was 50m high when a stone was dropped, find its height when the stone hits the ground. [ 68.5 m]
135. A football is kicked horizontally with uniform velocity towards a vertical wall. If the ball rebound after colliding at the wall with same velocity, draw (i) speed – time (ii) velocity – time curve.

136. Human body can survive a negative acceleration trauma incident if the magnitude of acceleration is less than 250 m/s2. If you are in automobile accident with a initial speed 105 km/hr and are stopped by an airbag that inflates from the dash-board, over what distance must the air bag stop you to survive the crash ?
[ 1.7 m ]
137. A canoe has velocity of 0.40 m/south-east relative to the earth. The canoe is on the river that is flowing 0.50 m/s east relative to the earth. Find the velocity of the canoe relative to the river. [ 0.354m/s, -52.50, south of west ]
138. A 8 kg ice block, released from the top of a 1.5 m long frictionless ramp, sliding downhill, reaching a speed of 2.5 m/s at the bottom. What is the angle between the ramp and the horizontal? If the coefficient of friction is 0.05, what is the new angle of inclination?

139. Thorium decays by the emission of alpha particle ( A = 4 ) to an isotopes of Radium ( A = 226 ). Calculate the ratio of the speed of the alpha particle to the radium and hence calculate recoil KE of the Radium if the ejected energy of the alpha particle is 4.6 MeV.
[113:2, 0.082 MeV]

140. A man of mass 70 kg is standing on a large sheet of frictionless ice and holding a large rock of mass 15 kg. In order to get off the ice, the man throws the rock at speed 12 m/s relative to earth at an angle 350 above the horizontal. What is his initial speed after he throw the rock ? [ 2.11 m/s]
141. Rain falls vertically onto a plane roof 1.5 m square, which is inclined to the horizontal at an angle of 300. The rain drops strike the roof with a vertical velocity of 3 m/s and a volume of 2.5 x 10-2 m3 of water is collected from the roof in one minute. Assuming that the conditions are steady and the velocity of raindrop after impact is zero, calculate (a) vertical force exerted on the roof by the impact of the rain and (b) pressure normal to the roof due to the impact of the of the rain. (c) If, instead, the roof were subject to a rain of hard spheres, which collided elastically, what would be the normal pressure on the roof then be? ( Density of water 1000 kg/m3) [1.25N, 0.48N/m2, 0.96Pa]
142. A fire engine pumps water at such a rate that the velocity of the water leaving the nozzle is 15 m/s. If the jet be directed perpendicularly on to a wall and rebound of the water be neglected, calculate the pressure on the wall. 1 m3 of water has mass 1000 kg. [ 2.25 x 105 N/m2]
143. In a nuclear collision, an alpha particle A of mass 4 unit is incident with velocity v on a stationary helium nucleus B of 4 mass unit. After collision, A moves in the direction BC with velocity v/2, where BC makes angle 600 with initial direction AB and the helium nucleus moves along BD. Calculate the velocity of rebound of the helium nucleus along BD and angle made with the direction AB. [ 0.87v, 300 ]
144. The diagram shows identical simple pendulums of length 0.8m . Bob A is raised with the string taut to the horizontal position A’ and released. Calculate (a) Velocity with which A strikes B. (b) velocities of A and B just after A makes a perfectly elastic collision with B. [ 4m/s, 4m/s]
145. Sand is deposited at rate 20 kg/s in a conveyor belt moving horizontally at 10m/min. Find (i) force required to maintain constant velocity, (ii) Power required to maintain constant velocity, (iii) Rate of change of KE of the sand. [10/3N, 5/9W, 5/18W]

146. Calculate the acceleration and tension in each case.

147. If coefficient of friction is 0.1, determine new acceleration in each case.

148. A bullet of mass 0.01 kg moving with velocity 500 m / s strikes a block of mass 2 kg which is suspended by a string of length 5 m. If the block rises the vertical height 0.1 m , calculate the emergent velocity of the bullet. [ 220 m/s]
149. According to ‘Chandrasekhar limit’ burnt-out star of size three times the solar mass undergoes into black hole. What is the radius of the event horizon?
150. Mass of sun is 330000 times greater than that of earth. For a person at the surface of earth, the average distance from the center of sun is 23500 times the distance to the center of the earth. What is the ratio of the sun’s gravitational force to that of earth’s?
151. Two people are carrying a uniform wooden board that is 3m long and weighs 160 N. If one person applies an upward force equal to 600 N at one end, at what point does the other person lift?
152. A mass X of 0.1 kg is attached to the free end of a vertical helical spring whose upper end is fixed and the spring is extended to 0.04m. X is now pulled down to 0.02 m and then released. Find its (i) Period, (ii) Maximum force during oscillation, (iii) Maximum KE. [0.4 sec, 0.5 N, 0.005 J]
153. A solid body floats with one-half of its volume outside the water and floats 3/8 of its volume outside in another liquid. What is the density of solid and liquid?
[ 0.5 and 0.8 g /cc ]
154. A disc of moment of inertia 0.1 kg m2 about its center and radius 0.2 m is released from rest on a plane inclined at 300 to the horizon. Calculate angular velocity after it has rolled 2m down the plane if its mass is 5 kg. [ 18.3 rad / s ]
155. What is the power output in horse power of an electric motor turning at 4800 rev/min and developing a torque of 4.30 Nm?
156. A braided nylon rope, 2.5 cm in diameter has a breaking strength of 1.24 x 105 N. Find the breaking strength of similar ropes 1.25 cm in diameter.
157. A compressed tank of rocket contains 0.25 m3 of kerosene, with mass 205 kg. The pressure at the top of the kerosene is 2.01 x 105 Pa. The kerosene exerts a force 16.4 N at the bottom of the tank, which has area 0.07 m2. Find the depth of the kerosene.
158. A soap bubble of in a vacuum has a radius 3 cm and another at vacuum has 6 cm. If the two bubbles coalesce under isothermal condition, calculate the radius of the formed bubble.
159. Water flows steadily along a uniform tube of cross-section 30 cm2. The static pressure is 1.2 x 105 Pa and the total pressure is 1.28 x 105 Pa. Calculate the flow velocity and the mass of the water per second flowing.
Revision
HSEB Exam Questions

160. A bullet of mass 20gm, moving with velocity 500 m/s passes through a wooden block of mass 100 kg, initially at rest. The bullet emerges out with a speed 100 m/s and the block slides 20 cm. Find coefficient of sliding friction. [ 0.16 ]
161. A ball of mass 4kg moving with a velocity 10 m/s collides with another body of mass 16 kg moving with 4 m/s in opposite direction. If both coalesce into a single body, determine loss of energy on impact. [ 313.6 J ]
162. A ball A of mass 0.1 kg moving with a velocity of 6 m/s collides with B of mass 0.2 kg at rest. Calculate their common velocity if both ball move off together. If A had rebounded with a velocity of 2 m/s, in the opposite direction, what would be the new velocity of B? [ 2m/s, 4m/s ]
163. A bullet of mass 20 g traveling horizontally at 100 m/s embeds in the wooden block of mass 1 kg which is suspended by vertical string of length 1m. Calculate the maximum inclination of the string. [ 36.10 ]
164. A car of mass 2000 kg moves at the speed 20 m/s along a horizontal road where the frictional force is 200 N. Calculate the power developed by the engine. If the car now travels in an inclined road of inclination 150, what will be the new power developed? [4 Kw,107 Kw]
165. A mass of gas emitted from the rear of toy rocket is initially 0.2 kg/s. If the speed of the gas relative to the rocket is 40 m/s, and the mass of the rocket is 4 kg, what is the initial acceleration of the rocket? [ 2 m/s2 ]

166. A disc rolling along a horizontal plane has a moment of inertia 4 kgm2 about its center and mass of 5 kg. The velocity along the plane is 2 m/s and radius is 2m, find (i) angular velocity (ii) total energy of the disc. [ 1rad/s, 12J ]
167. A roller whose diameter is 1m weights 360N. What horizontal force is necessary to pull the roller over the brick 0.1m high when the force is applied at the center? [ 270 N ]
168. A 200 kg satellite is lifted to an orbit of 2.2×104 km radius. If radius and mass of the earth are 6400km and 6 x 1024 kg respectively, how much additional PE is required to lift the satellite? [ 8.87 x 109 J ]
169. The density of ice is 971 kg/m3 and the density of sea water is 1025 kg/m3. What fraction of iceberg is beneath the water surface? [ 0.947 : 1 ]
170. An iceberg having volume 2060 cc floats in sea water of density 1030 kg/m3 with a portion of 224 cc above the surface. Calculate the density of the ice. [ 0.89 g/cc ]
171. A bullet of mass 10g is fired from a gun of mass 1 kg with a velocity of 100 m/s. Calculate the ratio of the KE of the bullet and the gun. [ 100:1]
172. A coin placed on a disc rotates with speed of 331/3 rev/min provided that the coin is not more than 10 cm from the axis. Calculate the coefficient of static friction.
173. Speed of a body spinning about an axis increases from rest to 100 rev/min in 5 sec if a constant of 20 NM is applied. The torque is removed and the body comes to rest 100 sec due to friction. Calculate the frictional torque.
174. A 25 cm thick block of ice floating on fresh water can support a 80 kg man standing on it. What is the smallest area of the ice block? ( Sp gravity of ice = 0.917)
175. A small mass rests on a horizontal platform which vibrates in a SHM with a period of 0.25 s. Find the maximum amplitude of the motion which will allow the mass to remain in contact with platform thought the motion.
176. Calculate the period of the revolution of the satellite revolving at a distance of 20 km from the earth surface. ( R = 6400km, g = 10 m/s2 ) [ 5050.13 s ]

177. A train of mass 2 x 105 kg moves with speed 72 km / hr up a straight inclined plane against a frictional force 1.28 x 104 N. The inclination is such that it rises vertically 1.0 m for every 100 m traveled along the inclination. Calculate (i) the rate of increase per second of PE, (ii) the power developed by the train. [ 400, 656 kw]
178. A constant torque of 500 Nm turns a wheel of moment of inertia 20 kgm2 about its center. Find the angular velocity and KE gained in 2 second and KE gained. [ 50 rad/s, 25000J]
179. A simple pendulum 4m long swings with amplitude of 0.2m. Determine (i) velocity at its lowest point, (ii) acceleration at the end of the path.
[ 0.32 m/s,0.5m/s2]
180. A piece of gold aluminum alloy weighs 100g in air and 80g in water. What is the weight of the gold in the alloy if the relative density of gold is 19.3 and that of aluminum is 2.5
181. An object of mass 8 kg is whirled round in a vertical circle of radius 2m with a speed 6m/s. Calculate the maximum and minimum tension in the string.
[ 224N, 64N]
182. A body is projected horizontally from the top of a tower of height 100m with a velocity 9.8 m/s. Find the velocity with which it hits the ground. [ 45.8 m/s ]
183. A particle of mass 0.3 kg vibrates with a velocity 2sec. If its amplitude is 0.5m, what is its maximum KE? [ 0.37 J ]
184. A string supports a solid Iron of mass 200g totally immersed in liquid of density 800kg/m3. If the density of the iron is 8000 kg/m3, calculate the tension in the string. [ 1.8 N ]
185. An object is dropped from the top of a tower of height 156.8 m and at the same time, another object is thrown vertically upward with velocity 78.4 m/s from the foot of the tower. When and where will they meet? [ 2s, 20m from top]
186. A constant torque of 200 Nm turns a wheel which has a moment of inertia 100 kg m2 about its center. Find KE gained after 20 revolutions. [
187. The displacement y of a mass vibrating with SHM is given by y = 20 sin 10t. Where y is in millimeter and t is in second. What is (a) amplitude (b) period (c) velocity when t = 0. [ 0.002m, 0.2 s, 0.682 m/s]
188. An alloy of mass 588 gm and volume 100 cc is made of iron of density 8.0 g/cc and aluminum of density 2.7 g/cc. Calculate the proportion by (i) volume, (ii) by mass of the constituents of the alloy.
[(i) 6×10-5 m3, 4×10-5 m3 (ii) 0.48kg, 0.108 kg]

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