Thermodynamics PYQs Set 5 (PDF)

Set 5 of 17 · Questions 121-150 of 484

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Mere Teacher · Previous Year Questions JEE Main Physics · Thermodynamics · Set 5 (Q121-150)
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121. $A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T . The mass ofeach molecule ofthe gas is m . Which ofthe following gives the density of the gas?$ (1) $P / (kT)$ (2) $Pm / (kT)$ (3) $P / (kT \nabla)$ (4) $mkT$ 122. $If an ideal flask containing hot coffee is shaken, the temperature of the coffee will:$ (1) $decrease$ (2) $increase$ (3) $remain same$ (4) $decrease if temperature is below 4ºC and increase if temperature is equal to or more than 4ºC$ 123. $One mole of ideal gas goes through a process p V^{3} = constant, where p and V are pressure and volume, respectively. Let W be the work done by the gas as its temperature is increased by Δ T . The value of \| W \| is (R is the universal gas constant.)$ (1) $R Δ T$ (2) $\frac{1}{3} R Δ T$ (3) $R^{3} Δ T$ (4) $\frac{R}{2} Δ T$ 124. $The length of a metal rod at 30^{\circ} C is 30 cm . If its temperature is raised to 105^{\circ} C, its length is increased by 0.027 cm . Then the coefficient of linear expansion of the metal is$ (1) $12 \times 10^{- 4} /° C$ (2) $12 \times 10^{- 5} /° C$ (3) $12 \times 10^{- 6} /° C$ (4) $12 \times 10^{- 7} /° C$ 125. $If a steam engine delivers 6.0 \times 1 0^{8} J of work per minute and absorbs 5.4 \times 1 0^{9} J of heat per minute from its boiler then efficiency of the engine is$ (1) $11%$ (2) $12%$ (3) $13%$ (4) $14%$ 126. $7 mole of certain monoatomic ideal gas undergoes a temperature increase of 40K at constant pressure. The increase in the internal energy of the gas in this process is (Given R = 8.3 J K^{- 1} m o l^{- 1})$ (1) $5810 J$ (2) $3486J$ (3) $11620J$ (4) $6972J$ 127. $In an adiabatic change, the pressure and temperature of a monatomic gas are related as P \propto T^{c}, where C equals$ (1) $\frac{3}{5}$ (2) $\frac{5}{3}$ (3) $\frac{2}{5}$ (4) $\frac{5}{2} .$ 128. $The moment of inertia I of uniform rod about a perpendicular bisector increases to I + Δ I, if the temperature is increased slightly by Δ T . If the coefficient of linear expansion is α, then \frac{Δ I}{I} is (Assume (\frac{Δ T}{T} ≪ 1)$ (1) $α Δ T$ (2) $2 α Δ T$ (3) $3 α Δ T$ (4) $4 α Δ T$ 129. $A source supplies heat to a system at the rate of 1000 W. If the system performs work at a rate of 200 W. The rate at which internal energy of the system increases is$ (1) $600W$ (2) $800 W$ (3) $500 W$ (4) $1200 W$ 130. $A Carnot engine operating between two reservoirs has efficiency \frac{1}{3} . When the temperature of cold reservoir raised by x, its efficiency decreases to \frac{1}{6} . The value of x, if the temperature of hot reservoir is 99° C, will be:$ (1) $16.5 K$ (2) $33 K$ (3) $66 K$ (4) $62 K$ 131. $A gas does 4.5 J of external work during adiabatic expansion. If its temperature falls by 2 K, then its internal energy will be$ (1) $increased by 4.5 J$ (2) $decreased by 4.5 J$ (3) $decreased by 2.25 J$ (4) $increased by 9.0 J$ 132. $When a monatomic gas expands at constant pressure, the percentages of heat supplied that is used to do external work and to increase its internal energy are respectively$ (1) $40,60$ (2) $25,75$ (3) $60,40$ (4) $75,25$ 133. $A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by 62ºC, the efficiency of the engine is doubled. The temperatures of the source and sink are-$ (1) $8 0^{0} C, 3 7^{0} C$ (2) $9 5^{0} C, 2 8^{0} C$ (3) $9 0^{0} C, 3 7^{0} C$ (4) $9 9^{0} C, 3 7^{0} C$ 134. $The conclusion of second law of thermodynamics is that$ (1) $No heat engine can have efficiency η equal to zero.$ (2) $No heat engine can have efficiency η equal to one.$ (3) $No heat engine can have efficiency η greater than one.$ (4) $No heat engine can have efficiency η less than one.$ 135. $An ideal gas at temperature T, pressure p occupies a volume V . If its temperature is halved and pressure doubled, what is its new volume?$ (1) $\frac{V}{4}$ (2) $\frac{V}{2}$ (3) $V$ (4) $2 V$ 136. $An ideal gas heat engine operates in a Carnot cycle between 22 7^{o} C and 12 7^{o} C . It absorbs 6 kcal at the higher temperature. The amount of heat (in kcal) converted into work is equal to$ (1) $4.8$ (2) $3.5$ (3) $1.6$ (4) $1.2$ 137. $One mole of an ideal diatomic gas expands from volume V to 2 V isothermally at a temperature 27^{\circ} C and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from 27^{\circ} C doing the same amount of work W, then its final temperature will be (close to)____^{\circ} C . (log_{e} 2 = 0.693)$ (1) $-30$ (2) $-189$ (3) $-117$ (4) $-56$ 138. $110joule of heat is added to a gaseous system whose internal energy is 40 J, then the amount of external work done is$ (1) $150 J$ (2) $70 J$ (3) $110 J$ (4) $40 J$ 139. $In which of the following processes, heat is neither absorbed nor released by a system? [NEET 2019]$ (1) $Adiabatic$ (2) $Isobaric$ (3) $Isochoric$ (4) $Isothermal$ 140. $Match the Cp/Cv ratio for ideal gase s with different type of molecules Molecule Type Cp/Cv (A) Monatomic (I) 7/5 (B) Diatomic rigid molecules (II) 9/7 (C) Diatomic non-rigid molecules (III) 4/3 (D) Triatomic rigid molecules (IV) 5/3$ (1) $(A) - (II), (B) - (III), (C) - (I), (D) - (IV)$ (2) $(A)-(IV),(B)-(II),(C)-(I),(D)-(III)$ (3) $(A) - (IV), (B) - (I), (C) - (II), (D) - (III)$ (4) $(A) - (III), (B) - (IV), (C) - (II), (D) - (I)$ 141. $The temperature of the earth without greenhouse effect will be$ (1) $0^{\circ} C$ (2) $- 18^{\circ} C$ (3) $- 10^{\circ} C$ (4) $- 24^{\circ} C$ 142. $An electric fan is switched on in a closed room. The air in the room is$ (1) $cooled$ (2) $heated$ (3) $maintains its temperature$ (4) $heated or cooled depending on the atmospheric pressure$ 143. $1.00 kg of liquid water at 100^{\circ} C undergoes a phase change into steam at 100^{\circ} C at 1.0 atm (take it to be 1.00 \times 10^{5} Pa). The initial volume of the liquid water was 1.00 \times 10^{- 3} m^{3} which is changed to 2.001 m^{3} of steam. Findthe change in the internal energy of the system. [Use heat of vaporization = 2000 kJ / kg]$ (1) $1800 kJ$ (2) $200 kJ$ (3) $2000 kJ$ (4) $180 kJ$ 144. $A piece of metal has a weight of 49 gm in air and 39 gm in a liquid of density 1.2 \times 10^{3} kg / m^{3} kept at 32^{\circ} C . When the temperature of the liquid is raised to 45^{\circ} C the metal piece has a weight of 40 gm . If the density of the liquid at 42^{\circ} C is 1.0 \times 10^{3} kg / m^{3}, then the coefficient of linear expansion of the metal is$ (1) $83\times 1 0^{- 3} /°C$ (2) $113\times 1 0^{- 3} /°C$ (3) $13\times 1 0^{- 4} /°C$ (4) $43\times 1 0^{- 3} /°C$ 145. $The molar specific heat at constant pressure of an ideal gas is (7/2) R . The ratio of specific heat at constant pressure to that at constant volume is$ (1) $9/7$ (2) $7/5$ (3) $8/7$ (4) $5/7.$ 146. $In a heat engine, the temperature of the source of sink are 500 K and 375 K. If the engine consumes 25 \times 1 0^{5} J per cycle, the work done per cycle is$ (1) $6.25 \times 1 0^{5} J$ (2) $3 \times 1 0^{5} J$ (3) $2.19 \times 1 0^{5} J$ (4) $4 \times 1 0^{4} J$ 147. $A sample of O . 1 g ofwater at 10 0^{o} C and normal pressure (1.013 \times 1 0^{5} N m^{- 2}) requires 54 cal of heat energy to convert to steam at 10 0^{o} C . Ifthe volume ofthe steam produced is 167.1 cc, the change in internal energy of the sample, is$ (1) $104.3 J$ (2) $208.7 J$ (3) $42.2 J$ (4) $84.5 J$ 148. $A monatomic gas at a pressure P, having a volume V expands isothermally to a volume 2 V and then adiabatically to a volume 16 V . The final pressure of the gas is (Take γ = 5/3)$ (1) $64 P$ (2) $32 P$ (3) $P/64$ (4) $16 P$ 149. $A heat engine operates between a cold reservoir at temperature T_{2} =400Kand a hot reservoir at temperature T_{1} . It takes 300J of heat from the hot reservoir and delivers 240J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be K.$ 150. $10 mole of oxygen is heated at constant volume from 30^{\circ} C to 40^{\circ} C . The change in the internal energy of the gas is____cal. (The molecular specific heat of oxygen at constant pressure, C_{P} = 7 cal / mol .^{\circ} C and R = 2 cal / mol .^{\circ} C .)$