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Question

The ratio of the isothermal elasticity of gas to its adiabatic elasticity is :

A
γ
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B
1γ
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C
1γ
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D
11γ
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Solution

The correct option is B 1γ
Elasticity is also defined using bulk modulus.
Bulk modulus is given by K=VdPdV
For an isothermal process, temperature is constant
PV=constant
d(PV)=0
PdV+dPV=0
P=VdPdV
So, for an isothermal process, buld modulus KT=P
For an adiabatic process,
PVγ=constant
d(PVγ)=0
dP.Vγ+P(γVγ1)dV=0
dP.Vγ+1+γPVγdV=0
γP=VdPdV
So, for an adiabatic process, bulk modulus Ks=γP
KTKs=PγP=1γ
Option B.

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