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Thermodynamic Potential NAT Level – 2 - IIT JAM MCQ

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10 Questions MCQ Test - Thermodynamic Potential NAT Level – 2

Thermodynamic Potential NAT Level – 2 for IIT JAM 2024 is part of IIT JAM preparation. The Thermodynamic Potential NAT Level – 2 questions and answers have been prepared according to the IIT JAM exam syllabus.The Thermodynamic Potential NAT Level – 2 MCQs are made for IIT JAM 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Thermodynamic Potential NAT Level – 2 below.

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*Answer can only contain numeric values

Thermodynamic Potential NAT Level – 2 - Question 1

For black body radiation, entropy varies with temperature as Find the value of α?

Detailed Solution for Thermodynamic Potential NAT Level – 2 - Question 1

For black body radiation,
(Stefan-Boltzman's lane)

The correct answer is: 3

*Answer can only contain numeric values

Thermodynamic Potential NAT Level – 2 - Question 2

For a fermi gas (in 8 dimension) value of the ratio C_p/C_V is?

Detailed Solution for Thermodynamic Potential NAT Level – 2 - Question 2

Average energy of Fermious is given by

pV^5/3= constant

The correct answer is: 1.667

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*Answer can only contain numeric values

Thermodynamic Potential NAT Level – 2 - Question 3

A quantity of heat ΔH is transferred from a large heat reservoir at temperature T to another large heat reservoir at temperature T/2. The heat reservoir have such large capacities that there is no observable change in true temperature. The ratio of the entropy change of the entire system to the entropy change in heat reservoir at temperature T/2 is?

Detailed Solution for Thermodynamic Potential NAT Level – 2 - Question 3

Now,
The correct answer is: 0.5

*Answer can only contain numeric values

Thermodynamic Potential NAT Level – 2 - Question 4

At high temperature, entropy of a spin half system is equal to Nk_B time the natural logarithm of what number?

Detailed Solution for Thermodynamic Potential NAT Level – 2 - Question 4

zcosh(βμH) = 1 and μHβ[tanh(βμH)] = 0
∴ Entropy for spin 1/2 system which given by
S = Nk[ln{2cosh(βμH)} – βμHtanh(βμH)]
Reduces to S = Nk_Bln 2
The correct answer is: 2

*Answer can only contain numeric values

Thermodynamic Potential NAT Level – 2 - Question 5

Virial of a system is defined as V = Σq_ip_i , where q_i is a generalized coordinate and p_i conjugate momentum. Value of V for a system consisting of N particles at temperature T is equal to aNk_BT. Find the value of constant a?

Detailed Solution for Thermodynamic Potential NAT Level – 2 - Question 5

Virial theorem states that
V = –2k·E
Since
⇒ V = –3NkT
⇒ a = –3
The correct answer is: -3

*Answer can only contain numeric values

Thermodynamic Potential NAT Level – 2 - Question 6

Entropy of a system of N classical harmonic oscillator having frequency ω and at temperature T is given by Find the value of constant x?

Detailed Solution for Thermodynamic Potential NAT Level – 2 - Question 6

For Harmonic oscillator

∴ Single Oscillator partition function

∴ N-oscillator partition function
Z = (Z₁ )N

∴ Helmholtz free energy function
F = –kTlnZ

∴ Entropy

∴ x = 1
The correct answer is: 1

*Answer can only contain numeric values

Thermodynamic Potential NAT Level – 2 - Question 7

The temperature of a cavity of fixed volume is doubled. Its energy increases by α times whereas number of photons increase by β times. Then calculate α/β?

Detailed Solution for Thermodynamic Potential NAT Level – 2 - Question 7

Energy of blackbody radiation αT⁴ and equilibrium number of photons in cavity αT³
The correct answer is: 2

*Answer can only contain numeric values

Thermodynamic Potential NAT Level – 2 - Question 8

For non interacting fermions entropy value with temperature for T → 0 as . Find the value of α.

Detailed Solution for Thermodynamic Potential NAT Level – 2 - Question 8

For T → 0 internal energy

⇒ α = 1
The correct answer is: 1

*Answer can only contain numeric values

Thermodynamic Potential NAT Level – 2 - Question 9

The mean internal energy of a one-dimensional harmonic oscillator in equilibrium with a heat bath of temperature T is in the units of k_BT.

Detailed Solution for Thermodynamic Potential NAT Level – 2 - Question 9

The correct answer is: 1

*Answer can only contain numeric values

Thermodynamic Potential NAT Level – 2 - Question 10

A system of N particles is enclosed in a volume V at a temperature T. The logarithm of the partition function is given by ln Z = N ln{V – bN}(k_BT)^3/2 , where b is a constant with approximate dimensions. The internal energy of the gas in the units of Nk_BT is given as?

Detailed Solution for Thermodynamic Potential NAT Level – 2 - Question 10

The correct answer is: 1.5

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