Adiabatic Relation Hard

Question

For adiabatic expansion of ideal gas, relation between T and V is:

RankGuru · Accepted Answer

From the basic adiabatic condition $P V^\gamma = Constant$ and the ideal gas law $PV = nRT$:
1. Substitute $P = \frac{nRT}{V}$ into the adiabatic equation:
$(\frac{nRT}{V}) V^\gamma = Constant$
2. $nRT V^{\gamma-1} = Constant$
3. Dividing by $nR$ (which is constant):
$T V^{\gamma-1} = Constant$.

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Adiabatic Relation Hard

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