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Isothermal and isentropic process are identical at

1. Saturation temperature
2. Critical temperature
3. Absolute zero temperature
4. Below 0°C temperature

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Correct Answer - Option 3 : Absolute zero temperature


For isentropic process:

\(\frac{T_2}{T_1}=\left(\frac{P_2}{P_1}\right)^{\frac{γ -1}{γ}}=\left(\frac{V_1}{V_2}\right)^{{γ -1}}\)

For isothermal process T1 = T2

\(\frac{T_2}{T_1}=\left(\frac{P_2}{P_1}\right)^{\frac{γ -1}{γ}}\)

\(1=\left(\frac{P_2}{P_1}\right)^{\frac{γ -1}{γ}}\)

\(\frac{γ -1}{γ}=0\)

γ = 1

γ is the ratio of specific heat at constant pressure Cp and constant volume Cv.

We know that for the difference in specific heat at constant pressure Cp and constant volume Cv is:

\(C_p-C_v=-T\left(\frac{\partial S}{\partial V}\right)_T\left(\frac{\partial S}{\partial P}\right)_T\)

At Absolute zero temperature dS = 0

∴ Cp - Cv = 0

Cp = Cv


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