Thermodynamics PYQs Set 16 (PDF)

Set 16 of 17 · Questions 451-480 of 484

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Mere Teacher · Previous Year Questions JEE Main Physics · Thermodynamics · Set 16 (Q451-480)
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451. $A piston of mass M is hung from a massless spring whose restoring force law goes as F = - k x^{3}, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with ' n' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T ) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height L_{0} to L_{1}, the total energy delivered by the filament is: (Assume spring to be in its natural length before heating)$ (1) $nRTln (\frac{L _{1}}{L _{0}}) + Mg (L_{1} - L_{0}) + \frac{3 k}{4} (L_{1}^{4}) (- L_{0}^{4})$ (2) $nRTln (\frac{L _{1}}{L _{0}}) + Mg (L_{1} - L_{0}) + \frac{k}{4} (L_{1}^{4} (- L_{0}^{4}))$ (3) $nRTln (\frac{L _{1}^{2}}{L _{0}^{2}}) + \frac{Mg}{2} (L_{1} - L_{0}) + \frac{k}{4} (L_{1}^{4} -) (L_{0}^{4})$ (4) $3 nRTln (\frac{L _{1}}{L _{0}}) + 2 Mg (L_{1} - L_{0}) + \frac{k}{3} (L (- L_{0}^{3})$ 452. $According to kinetic theory of gases, at absolute zero of temperature$ (1) $water freezes$ (2) $liquid helium freezes$ (3) $molecular motion stops$ (4) $liquid hydrogen freezes$ 453. $Which of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning.$ (1) (2) (3) (4) 454. $An ideal gas A and a real gas B have their volumes increased from V to 2 V under isothermal conditions. The increase in internal energy$ (1) $will be same in both A and B$ (2) $will be zero in both the gases$ (3) $of B will be more than that of A$ (4) $of A will be more than that of B$ 455. $A copper rod of length 75 cm and an iron rod of length 125 cm are joined together end to end. Both are of circular cross-section with diameter 2 cm . The free ends of the copper and iron are maintained at 100^{\circ} C and 0^{\circ} C respectively. The surfaces of the bars are insulated thermally. The temperature of the copper-iron junction is [Thermal conductivity of copper is 386.4 W / m - K and thermal conductivity of iron is 48.46 W / m - K]$ (1) $100^{\circ} C$ (2) $0^{\circ} C$ (3) $93^{\circ} C$ (4) $50^{\circ} C$ 456. $The relation between efficiency η of a heat engine and the coefficient of performance α of a refrigerator is$ (1) $η = \frac{1}{1 - α}$ (2) $η = \frac{1}{1 + α}$ (3) $η = 1 + α$ (4) $η = 1 - α$ 457. $At 0K which of the following properties of a gas will be zero?$ (1) $vibrational energy$ (2) $density$ (3) $kinetic energy$ (4) $potential energy.$ 458. $In a adiabatic process, relation between Δ U and Δ W is$ (1) $Δ U = Δ W$ (2) $Δ U = - Δ W$ (3) $Δ U = - Δ W + Δ Q$ (4) $Δ Q = Δ W$ 459. $A cycle tyre bursts suddenly. What is the type of this process?$ (1) $Isochoric$ (2) $Isothermal$ (3) $Isobaric$ (4) $Adiabatic$ 460. $Which of the following is not thermodynamically function?$ (1) $Enthalpy$ (2) $Work done$ (3) $Gibb’s energy$ (4) $Internal energy$ 461. $A thermodynamic process is shown in the figure. The pressure and volumes corresponding to some points in the figure are P_{A} = 3 \times 1 0^{4} Pa; V_{A} = 2 \times 1 0^{- 3} m^{3}; P_{B} = 8 \times 1 0^{4} Pa; V_{D} = 5 \times 1 0^{- 3} m^{3} . In the process AB, 600 J of heat is added to the system and in process BC, 200 J ofheat is added to the system. The change in internal energy of the system is process AC would be$ (1) $560 J$ (2) $800 J$ (3) $600 J$ (4) $640 J$ 462. $Isothermal process is the graph between$ (1) $pressure and temperature$ (2) $pressure and volume$ (3) $volume and temperature$ (4) $pV and temperature$ 463. $Which of the following processes described below is irreversible?$ (1) $The increase in temperature of an iron rod by hammering it.$ (2) $A gas in a small container at a temperature T_{1} is brought in contact with a big reservoir at a higher temperature T_{2} which increases the temperature of the gas.$ (3) $An ideal gas is enclosed in a piston cylinder arrangement with adiabatic walls.$ (4) $All of above$ 464. $The correct relation between γ = \frac{C _{p}}{C _{v}} and temperature T is:$ (1) $γ \propto \frac{1}{T}$ (2) $γ \propto T^{0}$ (3) $γ \propto \frac{1}{T}$ (4) $γ \propto T$ 465. $An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is S_{1} and that ofthe other part is S_{2} . Given that S_{1} > S_{2} . If the piston is removed then the total entropy of the system will be:$ (1) $S_{1} \times S_{2}$ (2) $S_{1} - S_{2}$ (3) $\frac{S _{1}}{S _{2}}$ (4) $S_{1} + S_{2}$ 466. $Starting with the same initial conditions, an ideal gas expands from volume V_{1} to V_{2} in three different ways. The work done by the gas is W_{1} if the process is purely isothermal. W_{2} . if the process is purely adiabatic and W_{3} if the process is purely isobaric. Then, choose the coned option$ (1) $W_{1} < W_{2} < W_{3}$ (2) $W_{2} < W_{3} < W_{1}$ (3) $W_{3} < W_{1} < W_{2}$ (4) $W_{2} < W_{1} < W_{3}$ 467. $A thermodynamic system is taken from state A to B along ACB and is brought back to A along BDA as shown in the PV diagram. The net work done during the complete cycle is given by the area$ (1) $P_{1} ACB P_{2} P_{1}$ (2) $ACBB’A’A$ (3) $ACBDA$ (4) $ADBB’A’A$ 468. $A poly-atomic molecule (C_{V} = 3 R, C_{P} = 4 R, where R is gas constant) goes from phase space point A (P_{A} = 10^{5} Pa, V_{A} = 4 \times 10^{- 6} m^{3}) to point B (P_{B} = 5 \times 10^{4} Pa, V_{B} = 6 \times 10^{- 6} m^{3}) to point C (P_{C} = 10^{4}) (Pa, V_{C} = 8 \times 10^{- 6} m^{3}) . A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is:$ (1) $500 R (ln 3 + ln 4)$ (2) $450 R (ln 4 - ln 3)$ (3) $500 R ln 2$ (4) $400 R ln 4$ 469. $Work done$ (1) $can only be positive$ (2) $can only be negative$ (3) $can either be positive or negative$ (4) $cannot be assigned a sign$ 470. $A measure of the degree of disorder of a system is known as$ (1) $Isobaric$ (2) $Isotropy$ (3) $Enthalpy$ (4) $Entropy$ 471. $First law of thermodynamics is consequence of conservation of$ (1) $work$ (2) $energy$ (3) $heat$ (4) $all of these$ 472. $The S.I. unit of specific heat capacity is$ (1) $J k g^{- 1} K^{- 1}$ (2) $J mol^{- 1} K^{- 1}$ (3) $J kg^{- 1}$ (4) $J K^{- 1}$ 473. $For hydrogen gas C_{P} - C_{\nabla} = a and for oxygen gas C_{P} - C_{\nabla} = b, so the relation between a and b is given by$ (1) $a = 16 b$ (2) $16 b = a$ (3) $a = 4 b$ (4) $a = b$ 474. $The first operation involved in a Carnot cycle is$ (1) $Isothermal expansion$ (2) $Adiabatic expansion$ (3) $Isothermal compression$ (4) $Adiabatic compression$ 475. $The efficiency of Carnot engine when source temperature is T_{1} and sink temperature is T_{2} will be$ (1) $\frac{T _{1} - T _{2}}{T _{1}}$ (2) $\frac{T _{2} - T _{1}}{T _{2}}$ (3) $\frac{T _{1} - T _{2}}{T _{2}}$ (4) $\frac{T _{1}}{T _{2}}$ 476. $The value of critical temperature in terms of van der Waals’ constant a and b is given by$ (1) $T_{c} = \frac{8 a}{27 Rb}$ (2) $T_{c} = \frac{27 a}{8 Rb}$ (3) $T_{c} = \frac{a}{2 Rb}$ (4) $T_{c} = \frac{a}{27 Rb} .$ 477. $Two objects made of the same material have masses ' m' and ' 2 m' and are at temperatures ' 2 T' and ' T' respectively. When heat ' Q' is supplied to the object of mass ' 2 m', its temperature raises to ' 2 T'. If the same heat is supplied to the object of mass ' m', its temperature raises to$ (1) $2 T$ (2) $3 T 2$ (3) $4 T$ (4) $3 T$ 478. $The freezer in a refrigerator is located at the top section so that$ (1) $the entire chamber of the refrigerator is cooled quickly due to convection$ (2) $the motor is not heated$ (3) $the heat gained from the environment is high$ (4) $the heat gained from the environment is low.$ 479. $Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal conductivites of these rods are: \frac{L _{A}}{L _{B}} = \frac{1}{2}, \frac{r _{A}}{r _{B}} = 2 and \frac{K _{A}}{K _{B}} = \frac{1}{2} . The free ends of rods A and B are maintained at 400 K, 200 K, respectively. The temperature of rods interface is ______K, when equilibrium is established.$ 480. $The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be J. (Given R = 8.31 J/mol.K)$