Thermodynamics PYQs Set 7 (PDF)

Set 7 of 17 · Questions 181-210 of 484

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Mere Teacher · Previous Year Questions JEE Main Physics · Thermodynamics · Set 7 (Q181-210)
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181. $A polyatomic gas with n degrees offreedom has a mean energy per molecule given by$ (1) $\frac{nkT}{N}$ (2) $\frac{nkT}{2 N}$ (3) $\frac{nkT}{2}$ (4) $\frac{3 kT}{2}$ 182. $A thermally insulated vessel with nitrogen gas at 27^{\circ} C is moving with a velocity of 100 ms^{- 1} . If the vessel is stopped suddenly, then the percentage change in the pressure of the gas is nearly (assume entire loss in KE of the gas is given as heat to gas and R = 8.3 Jmol^{- 1} K^{- 1})$ (1) $1.1$ (2) $0.93$ (3) $0.5$ (4) $2.25$ 183. $A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40°C, its efficiency increases by 30%. The temperature of the source will be:$ (1) $166.7K$ (2) $255. IK$ (3) $266.7 K$ (4) $367.7 K$ 184. $Latent heat of vaporization of water is 22.6 \times 10^{5} J / kg . The amount of heat needed to convert 100 kg of water at 100^{\circ} C into vapour at 100^{\circ} C is$ (1) $11.3 \times 10^{5} J$ (2) $11.3 \times 10^{6} J$ (3) $22.6 \times 10^{6} J .$ (4) $22.6 \times 10^{7} J$ 185. $The ratio of the slopes of isothermal and adiabatic curves is$ (1) $1$ (2) $γ$ (3) $\frac{1}{γ}$ (4) $\frac{3}{2}$ 186. $A scientist says that the efficiency of his heat engine which work at source temperature 12 7^{o} C and sink temperature 2 7^{o} C is 26%, then$ (1) $it is impossible$ (2) $it is possible but less probable$ (3) $it is quite probable$ (4) $data are incomplete.$ 187. $An ideal refrigerator has freezer at a temperature of - 13^{\circ} C . The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) is$ (1) $320^{\circ} C$ (2) $39^{\circ} C$ (3) $325 K$ (4) $325^{\circ} C$ 188. $The initial pressure and volume of an ideal gas are P_{0} and V_{0} . The final pressure of the gas when the gas is suddenly compressed to volume \frac{V _{0}}{4} will be: (Given γ = ratio of specific heats at constant pressure and at constant volume.)$ (1) $P_{0} (4)^{γ}$ (2) $4 P_{0}$ (3) $P_{0}$ (4) $P_{0} (4)^{\frac{1}{γ}}$ 189. $An ideal heat engine working between temperature T_{1} and T_{2} has an efficiency η, the new efficiency if both the source and sink temperature are doubled, will be$ (1) $\frac{η}{2}$ (2) $η$ (3) $2 η$ (4) $3 η$ 190. $A Carnot engine, having an efficiency of η = 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is$ (1) $99 J$ (2) $90 J$ (3) $1 J$ (4) $100 J$ 191. $Match List - I with List - II. List-I (A) Isobaric (B) Isochoric (C) Adiabatic (D) Isothermal List - II (I) Δ Q = Δ W (II) Δ Q= Δ U (III) Δ Q= zero (IV) Δ Q = Δ U + P Δ V Δ Q= Heat supplied Δ W = Work done by the system Δ U = Change in internal energy P = Pressure of the system Δ V = Change in volume of the system Choose the correct answer from the options given below:$ (1) $(A)-(IV), (B)-(I), (C)-(III), (D)-(II)$ (2) $(A)-(IV), (B)-(II), (C)-(III), (D)-(I)$ (3) $(A)-(IV), (B)-(III), (C)-(II), (D)-(I)$ (4) $(A)-(II), (B)-(IV), (C)-(III), (D)-(I)$ 192. $A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by: (R = universal gas constant)$ (1) $\frac{M v ^{2}}{7 R}$ (2) $\frac{M v ^{2}}{5 R}$ (3) $2 \frac{M v ^{2}}{7 R}$ (4) $7 \frac{M v ^{2}}{5 R}$ 193. $The temperature of sink of Carnot engine is 2 7^{o} C . Efficiency of engine is 25%. Then temperature of source is$ (1) $22 7^{o} C$ (2) $32 7^{o} C$ (3) $12 7^{o} C$ (4) $2 7^{o} C$ 194. $A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is γ = \frac{3}{2}, then the work done by the gas in the process is:$ (1) $\frac{R}{T} [2 - 2]$ (2) $\frac{T}{R} [2 + 2]$ (3) $RT [2 - 2]$ (4) $RT [2 + 2]$ 195. $In a thermodynamic system Δ U represents the increase in its internal energy and dW is the work done by the system then correct statement out of the following is$ (1) $Δ U = dW is an isothermal process$ (2) $Δ U = - dW is an adiabatic process$ (3) $Δ U = - dW is an isothermal process$ (4) $Δ U = dW is an adiabatic process.$ 196. $A thermocol box has a total wall area (including the lid) of 1.0 m^{2} and wall thickness of 3 cm . It is filled with ice at 0^{\circ} C . If the average temperature outside the box is 30^{\circ} C throughout the day, the amount of ice that melts in one day is [Use K_{thermocol} = 0.03 W / mK, L_{fusion (ice)} = 3.00 \times 10^{5} J / kg]$ (1) $1 kg$ (2) $2.88 kg$ (3) $25.92 kg$ (4) $8.64 kg$ 197. $The relation between absolute temperature (T) and pressure (P) of a gas in an adiabatic process is$ (1) $p^{γ} T^{1 - γ} = constant$ (2) $p^{1 - γ} T^{γ} = constant$ (3) $p^{γ - 1} T^{γ} = constant$ (4) $p^{γ} T^{γ - 1} = constant$ 198. $A carnot engine whose efficiency is 40 %, receives heat at 500 K . If the efficiency is to be 50 %, the source temperature for the same exhaust temperature is$ (1) $900 K$ (2) $600 K$ (3) $700 K$ (4) $800 K$ 199. $A rod is found to be 0.05 cm longer at 40^{\circ} C than it is at 10^{\circ} C . The length of the rod at 0^{\circ} C is (coefficient of linear expansion of the material of the rod = 1.5 \times 10^{- 5} ° C^{- 1})$ (1) $101.1 cm$ (2) $120.2 cm$ (3) $105.1 cm$ (4) $111.1 cm$ 200. $1 g of water of volume 1 cm^{3} at 100^{\circ} C is converted into steam at same temperature under normal atmospheric pressure = (= 1 \times 10^{5} Pa) . The volume of steam formed equals 1671 cm^{3} . If the specific latent heat of vaporisation of water is 2256 J / g, the change in internal energy is [NEET 2019]$ (1) $2423 J$ (2) $2089 J$ (3) $167 J$ (4) $2256 J$ 201. $An ideal gas heat engine operates in Carnot cycle between 227°C and 127°C. It absorbs 6 \times 1 0^{4} cals of heat at higher temperature. Amount of heat converted to work is$ (1) $2.4 \times 1 0^{4} cal$ (2) $6 \times 1 0^{4} cal$ (3) $1.2 \times 1 0^{4} cal$ (4) $4.8 \times 1 0^{4} cal$ 202. $1 g of water at 100^{\circ} C is completely converted into stream at 100^{\circ} C . 1. g of steam occupies a volume of 1650 cc . (Neglect the volume of 1 g of water at 100^{\circ} C). At the pressure of 10^{5} N / m^{2}, latent heat of steam is 540 cals / g ( 1 calorie = 4.2 joule ). The increase in the internal energy (in joule) is$ (1) $2310$ (2) $2103$ (3) $1650$ (4) $2150$ 203. $A carnot engine works between ice point and steam point. It is desired to increase efficiency by 20%, by changing temperature of sink to -$ (1) $253 K`$ (2) $293 K$ (3) $303 K$ (4) $243 K$ 204. $In thermodynamic processes which of the following statements is not true?$ (1) $In an isochoric process pressure remains constant.$ (2) $In an isothermal process the temperature remains constant.$ (3) $In an adiabatic process P V^{γ} = constant.$ (4) $In an adiabatic process the system is insulated from the surroundings.$ 205. $The temperature inside a refrigerator is t_{2}^{o} C and the room temperature is t_{1}^{o} C . The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be$ (1) $\frac{t _{1}}{t _{1} - t _{2}}$ (2) $\frac{t _{1} + 273}{t _{1} - t _{2}}$ (3) $\frac{t _{2} + 273}{t _{1} - t _{2}}$ (4) $\frac{t _{1} + t _{2}}{t _{1} + 273}$ 206. $A diatomic gas (γ = 1.4) does 100 J of work in an isobaric expansion. The heat given to the gas is:$ (1) $250 J$ (2) $150 J$ (3) $350 J$ (4) $490 J$ 207. $A 210 W heater is used to heat 100 g water. The time required to raise the temperature of this water from 25^{\circ} C to 100^{\circ} C is (specific heat capacity of water = 4200 J / Kg -^{\circ} C)$ (1) $100 s$ (2) $125 s$ (3) $150 s$ (4) $200 s$ 208. $A sample of gas at temperature T is adiabatically expanded to double its volume. The work done by the gas in the process is (given, γ = \frac{3}{2})$ (1) $W = TR (2 - 2)$ (2) $W = \frac{T}{R} (2 - 2)$ (3) $W = \frac{R}{T} (2 - 2)$ (4) $W = RT (2 - 2)$ 209. $The mean free path of molecules of a gas, (radius r) is inversely proportional to$ (1) $r^{3}$ (2) $r^{2}$ (3) $r$ (4) $r$ 210. $Two metal rods A and B each of length 50 cm and diameter 4.0 mm are joined together at temperature 30^{\circ} C . What is the change in length of the combined rod at 230^{\circ} C ? [Given linear expansion coefficients of rods A and B are respectively, 2.0 \times 10^{- 5} /° C and (1.0 \times 10^{- 5} /° C)$ (1) $4 mm$ (2) $2 mm$ (3) $3 mm$ (4) $1 mm$