(D) For an adiabatic process,the relationship between pressure $(P)$ and volume $(V)$ is given by $PV^\gamma = \text{constant}$.From the ideal gas equ

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

(D) For an adiabatic process,the relationship between pressure $(P)$ and volume $(V)$ is given by $PV^\gamma = \text{constant}$.From the ideal gas equation,$PV = RT$,we can write $V = \frac{RT}{P}$.Substituting this into the adiabatic equation:$P \left( \frac{RT}{P} \right)^\gamma = \text{constant}$$P \cdot \frac{T^\gamma}{P^\gamma} = \text{constant}$$P^{1-\gamma} T^\gamma = \text{constant}$.Therefore,the correct option is $D$.

Class 11 Physics Thermodynamics Adiabatic Process

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An ideal gas,undergoing adiabatic change,has which of the following pressure-temperature relationships?

AIPMT 1996 All AIPMT

A
$P^\gamma T^{1-\gamma} = \text{constant}$
B
$P^\gamma T^{\gamma-1} = \text{constant}$
C
$P^{\gamma-1} T^\gamma = \text{constant}$
D
$P^{1-\gamma} T^\gamma = \text{constant}$

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An ideal gas,undergoing adiabatic change,has which of the following pressure-temperature relationships?

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