Question

Which of the following statement is correct regarding $p-V$ graph?
1. Slope of $p-V$ graph in an isothermal process $s-\frac{p}{V}$
2. Slope of $p-V$ graph in an adiabatic process is $-\frac{p}{V}$.
3. Slope of $p-V$ graph in an isochoric process is $-\frac{\gamma P}{V}$
4. Slope of $p-V$ graph in an isobaric process is zero.

• A. $1,3,4$ are correct
• B. 2,3 are correct
• C. 1,4 are correct
• D. $2,3,4$ are correct

Answer 1

Answer: (C)

(i) and (iv) options are correct.
(i) Slope of $p$ - $V$ graph in an isothermal process is
$-\frac{p}{V}$ this is correct.

For isothermal process,
slope of $p$ - $V^{\prime }$ curve $\frac{dp}{dV}=-\frac{p}{V}$
(ii) Slope of $p-V$ group in an adiabatic process is $-\frac{p}{V}$, which is wrong.

Because slope of $p$ - $V$ graph in an adiabatic
process is$-\frac{\gamma p}{V}$
(iii) Slope of $p-V$ graph in an isochoric process is
$-\frac{\gamma p}{V}$ this option is wrong.
Because slope of $p-V$ graph for isochoric process is
$\frac{dp}{-\frac{dV}{V}}-\frac{dV}{V}=\frac{dp}{0}=\infty$

(d) Slope of $p-V$ graph in an isobaric process is zero. This option is correct.

$p-V$ curve is a straight line parallel to volume axis, slope of $p$ - $V$ curve for an isobaric process $\frac{dp}{dV}=0$