Question

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Answer 1

Explanation:

$\huge\blue{\underline{\underline{\bf Question:-}}}$

If a gas expands adiabatically such that TV^(¼)= k (k = constant) then value of (C.p.m/C.v.m) of the gas will be?

$\huge\blue{\underline{\underline{\bf Answer:-}}}$

$\huge{We \: \: know, } \\ \\ \frac{Cp}{Cv} = \gamma$

Here given that:-

$\\ \\ \boxed{ T {V}^{( \frac{1}{4} )} = constant} \\ \\ we \: \: know \: \: that \: \: for \: \: adiabatic \\ \\ \boxed{T {V}^{( \gamma - 1)} = constant} \\ \\ comparing \: \: the \: \: equations... \\ \\ \gamma - 1 = \frac{1}{4} \\ \\ \gamma = \frac{1}{4} + 1 \\ \\ \huge\boxed{ \leadsto \gamma = \frac{5}{4} }$

Answer 2

For adiabatic process:-

TV γ−1 = constant

Given:-

T∝V -½

⇒TV½ = constant

⇒γ−1=1/2

⇒γ=3/2=1.50

⇒γ=5 upon 4

hope it helps you .