(A) For an adiabatic process, the equation of state is given by $p V^\gamma = \text{constant}$.Using the ideal gas law $pV = nRT$, we can substitute $

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

(A) For an adiabatic process, the equation of state is given by $p V^\gamma = \text{constant}$.Using the ideal gas law $pV = nRT$, we can substitute $V = \frac{nRT}{p}$ into the adiabatic equation:$p \left( \frac{nRT}{p} \right)^\gamma = \text{constant}$$p \cdot p^{-\gamma} \cdot T^\gamma = \text{constant}$$p^{1-\gamma} T^\gamma = \text{constant}$.Thus, option $A$ is correct.

Class 11 Physics Thermodynamics Adiabatic Process

Medium

Which of the following is true in the case of an adiabatic process, where $\gamma = C_p / C_V$?

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

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Which of the following is true in the case of an adiabatic process, where $\gamma = C_p / C_V$?

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