NEET Physics Question - Thermal Physics

An ideal gas, undergoing adiabatic change, has which of the following pressure temperature relationship? (1996)

$P T^\gamma = \text{constant}$

$P^{1-\gamma} T^\gamma = \text{constant}$

$P^{\gamma-1} T = \text{constant}$

$P^{1-\gamma} T^{1-\gamma} = \text{constant}$

Solution:

From the adiabatic relation $PV^\gamma = \text{constant}$ and the ideal gas law $PV = nRT$, eliminating volume yields $P^{1-\gamma} T^\gamma = \text{constant}$.

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