For an adiabatic process, choose the correct relation

For an adiabatic process, the relation between pressure and volume is given by:

$PV^{\gamma} = \text{constant}$

From the ideal gas equation, we have $PV = nRT$, which gives $V = \dfrac{nRT}{P}$.

Substituting the value of $V$ in the adiabatic equation, we get:

$P \left(\dfrac{nRT}{P}\right)^{\gamma} = \text{constant}$

Since $nR$ is a constant, this simplifies to:

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

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