Question

Four curves A, B, C and D are drawn for given mass of gas. The curves which represent adiabatic and isothermal expansion are respectively

• A. A and B
• B. C and D
• C. B and A
• D. D and C

Answer 1

The correct option is A A and B

For an isothermal process $PV=constant$

Differentiating we get
$PdV+VdP=0$
or
$\frac{dP}{dV}=-\frac{P}{V}$
or
$\tan \theta =\frac{dP}{dV}=-\frac{P}{V}$-----------------------(i)

For a adiabatic process, we have
$P{V}^{\gamma }=constant$
Differentiating we get
$dPV\gamma +P\gamma V^{\gamma -1}=0$
or
$\frac{dP}{dV}=-\gamma \frac{P{V}^{\gamma -1}}{V^{\gamma }}=-\gamma (\frac{P}{V})$
Thus slope is $\tan \theta =\frac{dP}{dV}=\gamma \frac{P}{V}$................(ii)

Thus, slope of adiabatic process is more than the slope of isothermal process.
Also as $P\propto \frac{1}{V}$. Thus. we get the answer as A.