A gas expand adiabatically at constant pressure such thatT- V-3-2- The value of - CpCv of the gas will be-

Given: nbsp; T∝ V^ 3/2 nbsp; T = kV^ 3/2 nbsp; nbsp;or k = T V^3/2....(1) We also know, For adiabatic process k = T V^γ 1....(2) where k= constant ...

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Standard XIII

Chemistry

First Law of Thermodynamics

A gas expand ...

Question

A gas expand adiabatically at constant pressure such that
$T \propto V^{\frac{- 3}{2}}$ . The value of $γ (\frac{C_{p}}{C_{v}}$ ) of the gas will be:

1.33

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1.5

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Solution

The correct option is B 2.5
Given: $T \propto V^{\frac{- 3}{2}}$
$T = k V^{\frac{- 3}{2}}$ or
$k = T V^{\frac{3}{2}}$ ....(1)

We also know,
For adiabatic process
$k = T V^{γ - 1}$ ....(2)
where $k =$ constant

equating both the equations we get,

$T V^{\frac{3}{2}} = T V^{γ - 1}$
$γ - 1 = \frac{3}{2}$
$γ = \frac{5}{2}$

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A gas expand adiabatically at constant pressure such that T∝V−32. The value of γ (CpCv) of the gas will be:

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