First slide

Different type of processes

Question

The variation of pressure P with volume V for an ideal monoatomic gas during an adiabatic process is shown in figure. At point A the magnitude of rate of change of pressure with volume is

Easy

A

$\large \frac{{3{P_o}}}{{5{V_o}}}$
B

$\large \frac{{5{P_o}}}{{3{V_o}}}$
C

$\large \frac{{3{P_o}}}{{2{V_o}}}$
D

$\large \frac{{5{P_o}}}{{2{V_o}}}$

Solution

$\large \gamma \, = \,1 + \frac{2}{f}\, \Rightarrow \,1 + \frac{2}{3}\, \Rightarrow \,\frac{5}{3}$
$\large \frac{{dp}}{{dv}}\, = \, - \frac{{\gamma P}}{v}\, = \, - \frac{5}{3}\frac{{3{P_o}}}{{2{V_o}}}$
$\large \therefore \,|\frac{{dP}}{{dv}}|\, = \,\frac{5}{2}\frac{{{P_o}}}{{{V_o}}}$

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