Thermodynamic Potential NAT Level – 1


10 Questions MCQ Test Topic wise Tests for IIT JAM Physics | Thermodynamic Potential NAT Level – 1


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This mock test of Thermodynamic Potential NAT Level – 1 for Physics helps you for every Physics entrance exam. This contains 10 Multiple Choice Questions for Physics Thermodynamic Potential NAT Level – 1 (mcq) to study with solutions a complete question bank. The solved questions answers in this Thermodynamic Potential NAT Level – 1 quiz give you a good mix of easy questions and tough questions. Physics students definitely take this Thermodynamic Potential NAT Level – 1 exercise for a better result in the exam. You can find other Thermodynamic Potential NAT Level – 1 extra questions, long questions & short questions for Physics on EduRev as well by searching above.
*Answer can only contain numeric values
QUESTION: 1

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?


Solution:

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

*Answer can only contain numeric values
QUESTION: 2

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?


Solution:


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

*Answer can only contain numeric values
QUESTION: 3

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}}.\)


Solution:

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

*Answer can only contain numeric values
QUESTION: 4

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


Solution:

1 atm = 105 N/m2
 = 106 dynes/cm2



The correct answer is: 0.007429

*Answer can only contain numeric values
QUESTION: 5

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.


Solution:


dT = 1K

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

*Answer can only contain numeric values
QUESTION: 6

Calculate the value of ΔH for an isothermal process?


Solution:

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

*Answer can only contain numeric values
QUESTION: 7

If Z be the partition function and N represent number of particles the chemical potential is given as  Find the value of α.


Solution:

dF = dU – pdV + µdN

Since F = –kT ln Z

⇒ α = –1
The correct answer is: -1

*Answer can only contain numeric values
QUESTION: 8

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?


Solution:

p = –2T + p0


ΔS = 1



The correct answer is: 0.5

*Answer can only contain numeric values
QUESTION: 9

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


Solution:

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

*Answer can only contain numeric values
QUESTION: 10

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?


Solution:

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