Thermodynamics PYQs Set 13 (PDF)

Set 13 of 16 · Questions 361-390 of 459

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Mere Teacher · Previous Year Questions NEET Physics · Thermodynamics · Set 13 (Q361-390)
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361. $Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio \frac{V _{a}}{V _{d}} and the ratio \frac{V _{b}}{V _{c}} is:$ (1) $\frac{V _{a}}{V _{d}} \neq = \frac{V _{b}}{V _{c}}$ (2) $\frac{V _{a}}{V _{d}} = \frac{V _{b}}{V _{c}}$ (3) $\frac{V _{a}}{V _{d}} = (\frac{V _{b}}{V _{c}})^{- 1}$ (4) $\frac{V _{a}}{V _{d}} = (\frac{V _{b}}{V _{c}})^{2}$ 362. $The cycle is shown in figure is followed by an engine made of one mole of perfect gas in a cylinder with a piston. The processes A to B and C to D are isochoric whereas process B to C and D to A are adiabatic, the work done by the engine in one cycle is (V_{A} = V_{B} = V, V_{C} = V_{D} = 2V and g = 5/3)$ (1) $[1 - 4^{3/2}] (P_{B} - P_{A}) V$ (2) $\frac{3}{2} [1 - 3^{2/3}] (P_{B} - P_{A}) V$ (3) $\frac{3}{2} [1 - 2^{-2/3}] (P_{B} - P_{A}) V$ (4) $\frac{5}{2} [1 - 2^{-2/3}] (P_{B} - P_{A}) V$ 363. $Three moles of an ideal monoatomic gas performs a cycle ABCDA as shown in the figure. The temperatures of the gas at the states A, B, C and D are 400 K, 800 K, 2400 K and 1200 K, respectively. The work done by the gas during this cycle is (R is universal gas constant)$ (1) $1200 R$ (2) $3600 R$ (3) $2400 R$ (4) $2000 R$ 364. $There are two vessels filled with an ideal gas where volume of one is double the volume of other. The large vessel contains the gas at 8 kPa at 1000 K while the smaller vessel contains the gas at 7 kPa at 500 K. If the vessels are connected to each other by a thin tube allowing the gas to flow and the temperature of both vessels is maintained at 600 K, at steady state the pressure in the vessels will be (in kPa).$ (1) $24$ (2) $4.4$ (3) $18$ (4) $6$ 365. $An aluminum rod of length 1 m and a steel rod of length 2 m both having same cross-sectional area, are soldered together end-to-end. The thermal conductivity of aluminum rod and steel rod is 200 Js^{- 1} m^{- 1} K^{- 1} and 50 Js^{- 1} m^{- 1} K^{- 1} respectively. The temperatures of the free ends are maintained at 300 K and 500 K . What is the temperature of the junction?$ (1) $322 K$ (2) $350 K$ (3) $367 K$ (4) $400 K$ 366. $In the cyclic process given in the P - V diagram, the work done is$ (1) $π (\frac{P _{2} - P _{1}}{2})^{2}$ (2) $π (\frac{V _{2} - V _{1}}{2})^{2}$ (3) $π (P_{2} V_{2} - P_{1} V_{1})$ (4) $\frac{π}{4} (P_{2} - P_{1}) (V_{2} - V_{1})$ 367. $A circular copper ring at 30^{\circ} C has a hole with an area of 9.98 cm^{2} . It is made to slip onto a steel rod of cross-sectional area of 10 cm^{2}, by raising the temperature of both ring and rod simultaneously by an amount Δ T . If the coefficient of linear expansion of copper and steel are 17 \times 10^{- 6} /° C and 11 \times 10^{- 6} /° C, then minimum value of Δ T should be$ (1) $167.6^{\circ} C$ (2) $133.3^{\circ} C$ (3) $83.3^{\circ} C$ (4) $249.9^{\circ} C$ 368. $One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure. The change in internal energy of the gas during the transition is$ (1) $20 kJ$ (2) $-20 kJ$ (3) $20 J$ (4) $-12 kJ$ 369. $The pressure of a gas changes linearly with volume from A to B as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be$ (1) $6J$ (2) $Zero$ (3) $-4.5J$ (4) $4.5J$ 370. $A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in figure. The heat exchanged by the engine with the surroundings at constant volume is (Take C_{V} = \frac{3}{2} R)$ (1) $(P_{B} - P_{A}) V_{A}$ (2) $\frac{1}{2} (P_{B} - P_{A}) V_{A}$ (3) $\frac{3}{2} (P_{B} - P_{A}) V_{A}$ (4) $\frac{5}{2} (P_{B} - P_{A}) V_{A}$ 371. $In the given (V - T) diagram, what is the relation between pressures P_{1} and P_{2} ?$ (1) $P_{2} < P_{1}$ (2) $Cannot be predicted$ (3) $P_{2} = P_{1}$ (4) $P_{2} > P_{1}$ 372. $The net work done by an ideal gas going through the cycle as shown in the P - V diagram below is$ (1) $0$ (2) $P_{1} V_{1}$ (3) $\frac{3}{2} P_{1} V_{1}$ (4) $\frac{1}{2} P_{1} V_{1}$ 373. $A system is taken from state a to state c by two paths adc and abc as shown in the figure. The internal energy at a is U_{a} = 10 J. Along the path adc the amount ofheat heat absorbed d Q_{1} = 50 J and the work obtained d W_{1} = 20 J whereas along the path abc the heat absorbed d Q_{2} = 36 J. The amount of work along the path abc is$ (1) $10 J$ (2) $12 J$ (3) $36 J$ (4) $6 J$ 374. $The P - V diagram of a Carnot's engine is shown in the graph below. The engine uses 1 mole of an ideal gas as working substance. From the graph, the area enclosed by the P - V diagram is [The heat supplied to the gas is 8000 J]$ (1) $1200 J$ (2) $2000 J$ (3) $3000 J$ (4) $1000 J$ 375. $A thermodynamic system undergoes a cyclic process ABC as shown in the diagram. The work done by the system per cycle is$ (1) $- 750 J$ (2) $750 J$ (3) $1250 J$ (4) $- 1250 J$ 376. $In the following p - V diagram the equation of state along the curved path is given by (V - 2)^{2} = 4 ap where a is a constant. The total work done in the closed path is$ (1) $+ \frac{1}{3 a}$ (2) $- \frac{1}{3 a}$ (3) $\frac{1}{2 a}$ (4) $- \frac{1}{a}$ 377. $An ideal gas is compressed to half its initial volume by means of several process. Which of the process results in the maximum work done on the gas?$ (1) $Adiabatic$ (2) $Isobaric$ (3) $Isochoric$ (4) $Isothermal$ 378. $A gas is taken through the cycle A \to B \to C \to A, as shown. What is the net work done by the gas?$ (1) $Zero$ (2) $- 2000 J$ (3) $2000 J$ (4) $1000 J$ 379. $An ideal gas is taken via path ABCA as shown in figure. The net workdone in the whole cycle is$ (1) $6 P_{1} V_{1}$ (2) $zero$ (3) $3 P_{1} V_{1}$ (4) $- 3 P_{1} V_{1}$ 380. $For a perfect gas, two pressures P_{1} and P_{2} are shown in figure. The graph shows:$ (1) $P_{1} > P_{2}$ (2) $P_{1} < P_{2}$ (3) $P_{1} - P_{2}$ (4) $Insufficient data to draw any conclusion$ 381. $Choose the correct statement for processes A ∖ & B shown in figure.$ (1) $PV^{γ} = k for process B and PV=k for process A.$ (2) $PV = k for process B and A .$ (3) $\frac{T ^{γ}}{p ^{γ - 1}} = k for process A and PV=k for process B.$ (4) $None of these$ 382. $The P - V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work doneduring an adiabatic process CD is (use γ = 1.4) :$ (1) $- 500 J$ (2) $- 400 J$ (3) $400 J$ (4) $200 J$ 383. $A gas in a closed container undergoes the cycle ABCA as shown in the figure. The net heat released by the gas after it has undergone 20 cycles is$ (1) $3 kJ$ (2) $2 kJ$ (3) $1.5 kJ$ (4) $4.5 kJ$ 384. $P-T diagram of an ideal gas having three different densities ρ_{1}, ρ_{2}, ρ_{3} (in three different cases) is shown in the figure. Which of the following is correct:$ (1) $ρ_{1} > ρ_{2}$ (2) $ρ_{2} < ρ_{3}$ (3) $ρ_{1} = ρ_{2} = ρ_{3}$ (4) $ρ_{1} < ρ_{2}$ 385. $An ideal gas is compressed to half its initial volume by means of several processes. Which of the process results in the maximum work done on the gas?$ (1) $Isochoric$ (2) $Isothermal$ (3) $Adiabatic$ (4) $Isobaric$ 386. $A thermodynamic system undergoes cyclic process ABCDA as shown in figure. The work done by the system in the cycle is$ (1) $P_{0} V_{0}$ (2) $2 P_{0} V_{0}$ (3) $P_{0} V_{0} L$ (4) $zero$ 387. $A thermodynamic system is taken through the cycle abcda. The work done by the gas along the path bc is [NEET 2024]$ (1) $Zero$ (2) $30 J$ (3) $-90 J$ (4) $-60 J$ 388. $In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A \to B and C \to D are T_{1} and T2 (T_{1} >T2) respectively. Choose the correct option out of the following for work done if processes BC and DA are adiabatic.$ (1) $W_{AB} = W_{DC}$ (2) $W_{AD} = W_{BC}$ (3) $W_{BC} + W_{DA} > 0$ (4) $W_{AB} < W_{CD}$ 389. $A composite slab is prepared with two different materials A and B . The relation between their coefficient of thermal conductivity and thickness is given as K_{A} = \frac{K _{B}}{2} and X_{A} = 2 X_{B}, respectively. If the temperature of faces of A and B are 75^{\circ} C and 50^{\circ} C respectively, what will be the temperature of common surface?$ (1) $75^{\circ} C$ (2) $50^{\circ} C$ (3) $55^{\circ} C$ (4) $125^{\circ} C$ 390. $A Carnot engine absorbs an amount Q of heat from a reservoir at an abosolute temperature T and rejects heat to a sink at a temperature of T/3. The amount of heat rejected is$ (1) $Q / 4$ (2) $Q / 3$ (3) $Q / 2$ (4) $2Q / 3$