Maxwell's Relations MCQ Level – 2


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QUESTION: 1

Ratio of the adiabatic coefficient of expansion which is  to the isobaric coefficient of expansion   is
Select one:

Solution:

Adiabatic volume coefficient of expansion,

Isobaric volume coefficient of expansion,



But, from Maxwell's relation





But 
and 

or 
or 
The correct answer is: 

QUESTION: 2

For a perfect gas Joule - Thomson cofficient µ is equal to
Select one:

Solution:

Joule - Thomson coefficient µ,

For 1 mole of perfect gas, the equation of state is pV = RT
Differentiating it with respect to T, taking P constant,
We have,  
or 
or  
Substituting this result in equation (1) we get,
Joule-Thomson coefficient, μ = 0
The correct answer is: 0

QUESTION: 3

Calculate under what pressure (atm) water would boil at 150°C. If the change in specific volume when 1 gram of water is converted into steam is 1676cc. Given, latent heat of vaporization of steam = 540 cal/g; J = 4.2×107 erg/cal and one atmosphere pressure = 106 dynes/cm2
Select one:

Solution:

Here, ∂H = 540 cal.
= 540 × 4.2 × 107 erg.
∂V = 1676cc
Boiling Temperature T = 373 K
Temperature when water is to be boil = 150°C
= 150 + 273 = 423 K.
∂T = 423 – 373 = 50 K
∂p = ?
Applying these value in the maxwell's thermodynamical relation



= 1.814 × 106 dynes/cm2
= 1.814 atmosphere
Therefore, the pressure at which water would boil at 150°C
= 1.814 + 1,000 = 2.814 atmospheric pressure.
The correct answer is: 2.814

QUESTION: 4

The normal boiling point of benzene is 80°C. The latent heat of vaporization is 380 Joule/g, density of vapour at boiling points is 4g/litre and that of the liquid 0.9g/cm3 then the boiling point of benzene under a pressure of 80 cm of mercury.
Select one:

Solution:

Here, change in pressure, dP = 80 – 76
= 4 cm of Hg
= 4 × 13.6 × 980 dynes/cm2
Normal Boiling point, T = 80°C]
= 80 + 273 = 353 K
L = 980 joule/g
= 380 × 107 erg/g.



= 1.233 K
=1.233°C
The boiling point of benzene at a pressure of 80 cm of Hg
= 80 + 1.233
= 81.233°C
The correct answer is: 81.233°C

QUESTION: 5

For the perfect gas,  is equal to
Select one:

Solution:

From the maxwell's relation


But dH = dU + pdV

or 
But from perfect gas equation
pV = RT

Putting in (1)


The correct answer is: 0

QUESTION: 6

For any substance, the ratio of adiabatic and isothermal elasticities which are   and  respectively is equal to :
Select one:

Solution:

Isothermal elasticity, 
Adiabatic elasticity 




But from the first four Maxwell's equation


∴ Substituting these values in equation (1)


The correct answer is: 

QUESTION: 7

If C1 and C2 represents the specific heat of a liquid and its saturated vapour respectively and L is the latent heat of the vapour then clausius latent heat equation is given by :
Select one:

Solution:

For a change of state from liquid to vapour
 ...(i)
Here S1 and S2 are the entropies in the liquid and vapour states respectively Differentiating equation (1) with respect to T.


This equation is known as clausius latent heat equation.
The correct answer is:  

QUESTION: 8

The Gibb’s function G in thermodynamics is defined as
G = H – TS
(where, H = Enthalpy, T = Temperature, S = Entropy)
In an isothermal, isobaric, reversible process, G
Select one:

Solution:

Condition for a change to occur in any processes
dU – TdS ≤ pdV
d(U + pV – TS) ≤ 0
d(H – TS) ≤ 0
as [H = U + pV]
G = H – TS
or dG ≤ 0
It means is isothermal, Isobaric and reversible process, dG = 0 or G = constant
The correct answer is: remains constant but not zero

QUESTION: 9

The thermodynamical relation expressing TdS equation
Select one:

Solution:

Let the entropy S of a thermodynamic system be a function of temperature T and volume v, i.e. S = f(T, V)
Since, dS is perfect differential, we can write

Multiplying by T, we get

For any substance, the specific heat at constant volume is given by

Using dQ = TdS
Also from Maxwell's equation, we have


The correct answer is: 

QUESTION: 10

The ratio of the adiabatic to the isochoric pressure coefficient of expansion is
Select one:

Solution:

Adiabatic pressure coefficient of expansion,

isochoric pressure coefficient of expansion.


But, From Maxwell's relation


The correct answer is:  

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