Question

A gas obeys the equation of state $P(V_m-b)=RT$ (The parameter b is a constant). The slope for an isochore will be:

• A. Negative
• B. Zero
• C. $\frac{R}{(V_m-b)}$
• D. $\frac{R}{P}$

Answer 1

The correct option is C $\frac{R}{(V_m-b)}$

A thermodynamic process taking place at constant volume is known as the isochoric process. It is also sometimes called as an isometric process or constant-volume process.
The isochore graph is

Gas obeys the gas equation,
$P(V_m-b)=RT$
$P=\frac{RT}{(V_m-b)}$
$\text{slope of a graph}=\left(\frac{dy}{dx}\right)$
$\therefore \text{slope of isochore}={\left(\frac{dP}{dT}\right)}_{V_m}=\frac{R}{(V_m-b)}$