Pressure-temperature relationship for an idea | vedclass

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

Vedclass · Accepted Answer

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

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(D) For an adiabatic process,the relationship between pressure $P$ and volume $V$ is given by $P V^{\gamma} = 	ext{constant}$.From the ideal gas equation,$PV = nRT$,we can express volume as $V = \frac{nRT}{P}$.Substituting this expression for $V$ into the adiabatic equation:$P \left( \frac{nRT}{P} ight)^{\gamma} = 	ext{constant}$.Since $n$ and $R$ are constants,we have $P \cdot \frac{T^{\gamma}}{P^{\gamma}} = 	ext{constant}$.This simplifies to $P^{1 - \gamma} T^{\gamma} = 	ext{constant}$.

Pressure-temperature relationship for an ideal gas undergoing adiabatic change is $\left( \gamma = C_p/C_v \right)$

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