Question

The relation between absolute temperature (T) and pressure (P) in adiabatic process is:

• A. \( P^\gamma T^{1 - \gamma} = \text{constant} \)
• B. \( P^{1 - \gamma} T^\gamma = \text{constant} \)
• C. \( P^{\gamma - 1} T^\gamma = \text{constant} \)
• D. (None)

Hint:

For adiabatic processes, derive T–P relation using ideal gas law and \( PV^\gamma = \text{const} \).

Answer 1

The Correct Option is B

From thermodynamics: For adiabatic process, \[ PV^\gamma = \text{const}, \quad PV = nRT \Rightarrow V \propto \frac{T}{P} \]
Substitute in: \( P \left(\frac{T}{P}\right)^\gamma = \text{const} \Rightarrow P^{1 - \gamma} T^\gamma = \text{const} \)