A gas expand adiabatically at constant pressure such thatT- V-1-2- The value of - Cp-mCv-m of the gas will be-

Given: nbsp; T∝ V^ 1/2 = nbsp;T = kV^ 1/2 = nbsp; nbsp;k = T V^1/2....(1) For adiabatic process, PV^γ = constant or nbsp; k = T V^γ 1....(2) equatin ...

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Standard XII

Chemistry

Relation between P, V, T, Gamma in Adiabatic Proceses

A gas expand ...

Question

A gas expand adiabatically at constant pressure such that
$T \propto V^{\frac{- 1}{2}}$ . The value of $γ (\frac{C_{p}, m}{C_{v}, m}$ ) of the gas will be:

1.3

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1.5

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Solution

The correct option is B 1.5
Given: $T \propto V^{\frac{- 1}{2}}$ = $T = k V^{\frac{- 1}{2}}$ = $k = T V^{\frac{1}{2}}$ ....(1)
For adiabatic process, $P V^{γ}$ = constant
or $k = T V^{γ - 1}$ ....(2)
equating both the equations we get,
$T V^{\frac{1}{2}} = T V^{γ - 1}$
$γ - 1 = \frac{1}{2}$
$γ = \frac{3}{2}$

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Relation between P, V, T, Gamma in Adiabatic Proceses

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