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Question

A certain ideal gas undergoes a polytropic process represented by equation PVn=constant. If Molar heat capacity for this process is negative and γ is a standard constant which denotes the ratio of the molar heat capacities of a gas, then the range of values of n will be

A
0<n<γ
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B
1<n<γ
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C
n=γ
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D
n>γ
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Solution

The correct option is B 1<n<γ
Molar heat capacity for a polytropic process [PVn=constant] is given by,
C=(Rγ1)(Rn1)
C=(nγ)R(n1)(γ1) ....(i)
For C (molar heat capacity) to be ve,
Since γ>1 always, thus C can be negative in two case.
Case 1:
(nγ)<0 and (n1)>0
This gives n<γ and n>1

Case 2:
(nγ)>0 and (n1)<0
This gives n>γ and n<1
But if γ>1 and n>γ, this means n>1. Hence this case is not possible.

Therefore for C to be negative, (n<γ) and (n>1) or (1<n<γ)

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