Thermodynamic Laws and Ensembles - Thermodynamics and Statistical Mechanics - Physics Previous Year Questions

1

2007 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2007

A heat pump working on the Carnot cycle maintains the inside temperature of a house at \( 22^\circ C \) by supplying \( 450 \text{ kJ s}^{-1} \). If the outside temperature is \( 0^\circ C \), the heat taken, in \( \text{kJ s}^{-1} \), from the outside air is approximately

A

487

B

470

C

467

D

417

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2

2007 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2007

The free energy for a photon gas is given by \( F = -\left( \frac{a}{3} \right) VT^4 \), where \( a \) is a constant. The entropy \( S \) and the pressure \( P \) of the photon gas are

A

\(S = \frac{4}{3} aVT^3, \; P = \frac{a}{3} T^4 \)

B

\(S = \frac{1}{3} aVT^3, \; P = \frac{4a}{3} T^3 \)

C

\(S = \frac{4}{3} aVT^3, \; P = \frac{a}{3} T^3 \)

D

\(S = \frac{1}{3} aVT^3, \; P = \frac{4a}{3} T^4 \)

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3

2007 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2007

The free energy for a photon gas is given by \( F = -\left(\frac{a}{3}\right)VT^4 \), where \( a \) is a constant.
The entropy \( S \) and the pressure \( P \) of the photon gas are

A

\(S = \frac{4}{3}aVT^3, \; P = \frac{a}{3}T^4 \)

B

\(S = \frac{1}{3}aVT^3, \; P = \frac{4a}{3}T^4 \)

C

\(S = \frac{4}{3}aVT^3, \; P = \frac{a}{3}T^4 \)

D

\(S = \frac{1}{3}aVT^3, \; P = \frac{4a}{3}T^4 \)

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4

2008 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2008

Thermodynamic variables of a system can be volume V, pressure P, temperature T, number of particles N, internal energy E and chemical potential $\mu$, etc. For a system to be specified by Microcanonical (MC), Canonical (CE) and Grand Canonical (GC) ensembles, the parameters required for the respective ensembles are:

A

MC: (N,V,T); CE: (E,V,N); GC: (V,T,$\mu$)

B

MC: (E,V,N); CE: (N,V,T); GC: (V,T,$\mu$)

C

MC: (V,T,$\mu$); CE: (N,V,T); GC: (E,V,N)

D

MC: (E,V,N); CE: (V,T,$\mu$); GC: (N,V,T)

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5

2009 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2009

The Helmholtz free energy of the system is given by

A

$-k_B T \ln\left(1 + e^{-\varepsilon/k_B T}\right)$

B

$k_B T \ln\left(1 + e^{-\varepsilon/k_B T}\right)$

C

$\frac{3}{2} k_B T$

D

$\varepsilon - k_B T$

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6

2010 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2010

The spectrum of radiation emitted by a black body at a temperature 1000 K peaks in the

A

Visible range of frequencies

B

Infrared range of frequencies

C

Ultraviolet range of frequencies

D

Microwave range of frequencies

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7

2010 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2010

Which among the following sets of Maxwell relations is correct? (U - internal energy, H - enthalpy, A - Helmholtz free energy and G - Gibbs free energy)

A

\(T = \left(\frac{\partial U}{\partial V}\right)_S \) and \(P = \left(\frac{\partial U}{\partial S}\right)_V \)

B

\(V = \left(\frac{\partial H}{\partial P}\right)_S \) and \(T = \left(\frac{\partial H}{\partial S}\right)_P \)

C

\(P = -\left(\frac{\partial G}{\partial V}\right)_T \) and \(V = \left(\frac{\partial G}{\partial P}\right)_T \)

D

\(P = -\left(\frac{\partial A}{\partial S}\right)_T \) and \(S = -\left(\frac{\partial A}{\partial P}\right)_V \)

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8

2011 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2011

A Carnot cycle operates on a working substance between two reservoirs at temperatures \( T_1 \) and \( T_2 \), with \( T_1 > T_2 \). During each cycle, an amount of heat \( Q_1 \) is extracted from the reservoir at \( T_1 \) and an amount \( Q_2 \) is delivered to the reservoir at \( T_2 \). Which of the following statements is INCORRECT?

A

work done in one cycle is \(Q_1 - Q_2 \)

B

\(\frac{Q_1}{T_1} = \frac{Q_2}{T_2} \)

C

Entropy of the hotter reservoir decreases

D

Entropy of the universe (consisting of the working substance and the two reservoirs) increases

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9

2011 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2011

A Carnot cycle operates on a working substance between two reservoirs at temperatures T₁ and T₂, with T₁ > T₂. During each cycle, an amount of heat Q₁ is extracted from the reservoir at T₁ and an amount Q₂ is delivered to the reservoir at T₂. Which of the following statements is INCORRECT?

A

work done in one cycle is Q₁ - Q₂

B

Q₁/T₁ = Q₂/T₂

C

entropy of the hotter reservoir decreases

D

entropy of the universe (consisting of the working substance and the two reservoirs) increases

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10

2011 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2011

If the isothermal compressibility of a solid is \( \kappa_T = 10^{-10} \text{ (Pa)}^{-1} \), the pressure required to increase its density by 1% is approximately

A

\(10^4 \text{ Pa} \)

B

\(10^6 \text{ Pa} \)

C

\(10^8 \text{ Pa} \)

D

\(10^{10} \text{ Pa} \)

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11

2011 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2011

If the isothermal compressibility of a solid is \( \kappa_T = 10^{-10} \ (\text{Pa})^{-1} \), the pressure required to increase its density by 1% is approximately

A

\(10^4 \ \text{Pa} \)

B

\(10^6 \ \text{Pa} \)

C

\(10^8 \ \text{Pa} \)

D

\(10^{10} \ \text{Pa} \)

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12

2012 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2012

The isothermal compressibility, $\kappa$ of an ideal gas at temperature $T_0$ and volume $V_0$ is given by

A

\(-\frac{1}{V_0} \frac{\partial V}{\partial P}|_{T_0}\)

B

\(\frac{1}{V_0} \frac{\partial V}{\partial P}|_{T_0}\)

C

-V_0 \frac{\partial P}{\partial V}|_{T_0}

D

V_0 \frac{\partial P}{\partial V}|_{T_0}

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13

2013 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2013

Two gases separated by an impermeable but movable partition are allowed to freely exchange energy. At equilibrium, the two sides will have the same

A

pressure and temperature

B

volume and temperature

C

pressure and volume

D

volume and energy

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14

2013 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2013

The entropy function of a system is given by \(S(E) = a E(E_0 - E)\) where \(a\) and \(E_0\) are positive constants. The temperature of the system is

A

negative for some energies

B

increases monotonically with energy

C

decreases monotonically with energy

D

Zero

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15

2014 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2014

For a gas under isothermal conditions, its pressure \(P\) varies with volume \(V\) as \(P \propto V^{-5/3}\). The bulk modulus \(B\) is proportional to

A

\(V^{-1/2}\)

B

\(V^{-2/3}\)

C

\(V^{-3/5}\)

D

\(V^{-5/3}\)

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16

2016 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2016

The total power emitted by a spherical black body of radius \(R\) at a temperature \(T\) is \(P_1\). Let \(P_2\) be the total power emitted by another spherical black body of radius \(R/2\) kept at temperature \(2T\). The ratio, \(P_1/P_2\) is __________. (Give your answer upto two decimal places)

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17

2016 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2016

\(N\) atoms of an ideal gas are enclosed in a container of volume \(V\). The volume of the container is changed to \(4V\), while keeping the total energy constant. The change in the entropy of the gas, in units of \(N k_B \ln 2\), is ________, where \(k_B\) is the Boltzmann constant.

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18

2017 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2017

A reversible Carnot engine is operated between temperatures \(T_1\) and \(T_2\) (\(T_2 > T_1\)) with a photon gas as the working substance. The efficiency of the engine is

A

\(1 - \frac{3T_1}{4T_2}\)

B

\(1 - \frac{T_1}{T_2}\)

C

\(1 - \left(\frac{T_1}{T_2}\right)^{3/4}\)

D

\(1 - \left(\frac{T_1}{T_2}\right)^{4/3}\)

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19

2017 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2017

The energy density and pressure of a photon gas are given by \(u = aT^{4}\) and \(P = u / 3\), where \(T\) is the temperature and \(a\) is the radiation constant. The entropy per unit volume is given by \(\alpha aT^{3}\). The value of \(\alpha\) is ______. (up to two decimal places).

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20

2018 · Physics · Thermodynamics and Statistical Mechanics · Thermodynamic Laws and Ensembles

Physics (PH) 2018

An air-conditioner maintains the room temperature at \(27 ^\circ \text{C}\) while the outside temperature is \(47 ^\circ \text{C}\). The heat conducted through the walls of the room from outside to inside due to temperature difference is \(7000 \text{ W}\). The minimum work done by the compressor of the air-conditioner per unit time is ______ \(\text{W}\).

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