Question

Isothermal and isentropic process are identical at

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

Answer 1

Correct Answer - Option 3 : Absolute zero temperature

Explanation:

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 C_p and constant volume C_v.

We know that for the difference in specific heat at constant pressure C_p and constant volume C_v 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

∴ C_p - C_v = 0

C_p = C_v

\(\frac{C_p}{C_v}=1\)