Question

Assertion :$C_P-C_V=R$ for an ideal gas. Reason: ${\left(\frac{\partial E}{\partial V}\right)}_T=0$ for an ideal gas.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

$C_v={\left(\frac{\partial E}{\partial T}\right)}_v⟶1$

For an ideal gas, $C_p-C_v=R$

From $\left(1\right)no.$ Equation, ${\left(\frac{\partial C_v}{\partial v}\right)}_T={\left(\frac{\partial }{\partial v}{\left(\frac{\partial E}{\partial T}\right)}_v\right)}_T={\left(\frac{\partial }{\partial T}{\left(\frac{\partial E}{\partial v}\right)}_T\right)}_v$

For an ideal gas ${\left(\frac{\partial E}{\partial v}\right)}_T=0$

$⟹{\left(\frac{\partial C_v}{\partial v}\right)}_T={\left(\frac{\partial }{\partial T}\right(0\left)\right)}_v=0$

But due to this $C_P-C_v=R$ is not reasoned.