JEE MainPhysicsModerateThermodynamics

An ideal gas obeys the law $PV^{x} =$ constant. x is value for
which it has zero molar specific heat at normal temperature. Then find 5
x. (Cv for the gas is 2.5 R)

Show answer and solution

For a gas at normal temperature,

\ c_{v} = \frac{5}{2}R

Specific heat for a polytropicprocess

C = C_{v} + \frac{R}{1 - x} = \frac{5}{2}R + \frac{R}{1 - x}

According to question C = 0

\frac{5(1 - x) + 2}{2(1 - x)} = 0\ or\ \frac{7 - 5x}{1 - x} = 0 \Rightarrow x = 1.4

Source: Grass-G / P-08 Physics paper 23 October.docx

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