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IIT JAM Exam  >  IIT JAM Tests  >  Thermodynamic Potential NAT Level – 1 - IIT JAM MCQ

Thermodynamic Potential NAT Level – 1 - IIT JAM MCQ


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10 Questions MCQ Test - Thermodynamic Potential NAT Level – 1

Thermodynamic Potential NAT Level – 1 for IIT JAM 2024 is part of IIT JAM preparation. The Thermodynamic Potential NAT Level – 1 questions and answers have been prepared according to the IIT JAM exam syllabus.The Thermodynamic Potential NAT Level – 1 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 – 1 below.
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Thermodynamic Potential NAT Level – 1 - Question 1
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A system of N localized, non-interacting spin 1/2 ions of magnetic moment in each is kept in an external  magnetic field H. If the system is in equilibrium at temperature T, the Helmholtz free energy of the system is given as   Calculate the value of α?


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

Partition function 
Vibrational partition function in this 
where 



For the whole system  Z(v) = [Z(v)]N
Helmholtz free energy F = –NkB TlnZ

⇒ α = 2
The correct answer is: 2

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Thermodynamic Potential NAT Level – 1 - Question 2
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The free energy of a photon gas enclosed in a volume V is given by  where a is the constant and T is the temperature of the gas.
The chemical potential of the photon gas is?


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


and  
No term depends on N
hence 
µ = 0
The correct answer is: 0

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Thermodynamic Potential NAT Level – 1 - Question 3
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Calculate the standard Gibb’s free energy change for the formation of methane from carbon and hydrogen at 298 K in the units of kJ/mol. Given that ΔH is –74.9 kJ/mol and ΔS = -80.75J{\rm{/K - mol}}.\)


Detailed Solution for Thermodynamic Potential NAT Level – 1 - Question 3

Given  ΔH = –74.9 kJ/mol
ΔS = –80.75 J/K-mol
Now use the equation
ΔS = ΔH – TΔS
⇒ ΔS = –74.9 kJ/mol +298 K (80.75/K-mol) × (1 kJ/1000J)
⇒ ΔS = – 50.9 kJ/mol
The correct answer is: -50.9

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Thermodynamic Potential NAT Level – 1 - Question 4
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Calculate the depression of melting point of ice (in K) produced by 1 atm increase of pressure, given that Lice = 80 cal gm-1 and specific volume of ice and water at 0°C are 1.091 cm3 and 1 cm3 respectively

Detailed Solution for Thermodynamic Potential NAT Level – 1 - Question 4

1 atm = 105 N/m2
 = 106 dynes/cm2



The correct answer is: 0.007429

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Thermodynamic Potential NAT Level – 1 - Question 5
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To change the melting point of ice by 1K, what should be the change in the pressure, given that L = 80 cal gm-1 and specific volume of ice and water at 0°C are 1 cm3 and 1.091 cm3 respectively. Give your answer in atm.

Detailed Solution for Thermodynamic Potential NAT Level – 1 - Question 5


dT = 1K

dp = 1.3525 × 108 dynes/cm2
⇒dp = 135.25 atm.
The correct answer is: 135.25

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Thermodynamic Potential NAT Level – 1 - Question 6
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Calculate the value of ΔH for an isothermal process?

Detailed Solution for Thermodynamic Potential NAT Level – 1 - Question 6

ΔH = Cp ΔT
ΔT = 0
⇒ ΔH = 0
The correct answer is: 0

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Thermodynamic Potential NAT Level – 1 - Question 7
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If Z be the partition function and N represent number of particles the chemical potential is given as  Find the value of α.

Detailed Solution for Thermodynamic Potential NAT Level – 1 - Question 7

dF = dU – pdV + µdN

Since F = –kT ln Z

⇒ α = –1
The correct answer is: -1

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Thermodynamic Potential NAT Level – 1 - Question 8
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A solid melts into liquid. The relation between the pressure p and the temperature T of the phase transition is P = –2T + P0 , the entropy charge associated with the phase transition is 1 Joule mol-1 K-1 . The Claussius-Clapeyron equation for the latent heat latent heat  then  is equal to?

Detailed Solution for Thermodynamic Potential NAT Level – 1 - Question 8

p = –2T + p0


ΔS = 1



The correct answer is: 0.5

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Thermodynamic Potential NAT Level – 1 - Question 9
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It the partition function of a harmonic oscillator with frequency  at temperature T in  then the free energy of 8 such independent oscillators in terms of  is

Detailed Solution for Thermodynamic Potential NAT Level – 1 - Question 9

The Helmholtz free energy N independent harmonic oscillator in terms of partition function Z is
F = –NkT ln Z
here 


N = 8

The correct answer is: 16

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Thermodynamic Potential NAT Level – 1 - Question 10
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A system of N non-interacting and distinguishable particles of spin1 is in thermodynamic equilibrium. The entropy of the system turns out to be of the form NkBln x. Find the value of x?

Detailed Solution for Thermodynamic Potential NAT Level – 1 - Question 10

Number of microstates  Ω = 3N
Entropy is given by 
∴ S = NKBln 3
⇒ x = 3
The correct answer is: 3

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