Question

A graph of pressure versus volume for an ideal gas for isochoric, isobaric, isothermal and adiabatic processes is given. Which one is for the adiabatic process?

• A. $OA$
• B. $OB$
• C. $OC$
• D. $OD$

Answer 1

The correct option is C $OC$


OA is an isobaric process.
OD is an isochoric process.

For,
isobaric $\to PV=$ const
Adiabatic $\to P{V}^{\gamma }=\mathrm{const}$

$\frac{dP}{dV}$ is the slope

$\frac{dP}{dV}=-\frac{P}{V}---\text{(i)}$ for isothermal process.

For adiabatic process
$P{V}^{\gamma }$= const

$P.\gamma V^{\gamma -1}dV+V^{\gamma }dP=0$
$P\cdot \gamma V^{\gamma }\cdot V^{-1}dV=-V^{\gamma }dP$
$⟹\frac{dP}{dV}=-\frac{\gamma P}{V}---\text{(ii)}$

From (i) and (ii) we can say OC is an adiabatic process.