In an adiabatic process wherein, pressure is increased by $$23$$% if $$CPCV=32$$, Then the volume decreases by about

$$P=cV$$−γ ∴ Δ$$PP=$$−γΔVV Δ$$VV=$$−$$1$$γΔPP $$=$$−$$23$$×$$23$$% $$=$$−$$49$$%

Different type of processes

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Question

In an adiabatic process wherein, pressure is increased by $\frac{2}{3} % if \frac{C_{P}}{C_{V}} = \frac{3}{2},$ Then the volume decreases by about

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Solution

$\begin{array}{l} P = {cV}^{- γ} \\ ∴ \frac{ΔP}{P} = - γ \frac{ΔV}{V} \\ \frac{ΔV}{V} = - \frac{1}{γ} \frac{ΔP}{P} \\ = - \frac{2}{3} \times \frac{2}{3} % \\ = - \frac{4}{9} % \end{array}$

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