Question

For a gas obeying the van der Waals' equation,at the critical temperature?

• A. both ${\left[\frac{\partial P}{\partial V}\right]}_T$ and ${\left[\frac{{\partial }^{2}P}{\partial V^2}\right]}_T$ are zero
• B. only ${\left[\frac{{\partial }^{2}P}{\partial V^2}\right]}_T$ is not zero
• C. ${\left[\frac{\partial P}{\partial V}\right]}_T$ is zero but ${\left[\frac{{\partial }^{2}P}{\partial V^2}\right]}_T$ is non- zero
• D. ${\left[\frac{\partial P}{\partial V}\right]}_T$ is non- zero but ${\left[\frac{{\partial }^{2}P}{\partial V^2}\right]}_T$ is zero

Answer 1

The correct option is A both ${\left[\frac{\partial P}{\partial V}\right]}_T$ and ${\left[\frac{{\partial }^{2}P}{\partial V^2}\right]}_T$ are zero

At critical temperature if you apply more pressure then the gas changes into liquid and so volume does not changes.

${\left(\frac{dP}{dV}\right)}_T$ and ${\left(\frac{d^{2}P}{d{V}^2}\right)}_T$ are both zero.