Question

One mole of oxygen is expanded from a volume 1 $\ell$ to 2$\ell$ at a constant temperature $T=280K$. Find the change in internal energy of the gas.

• A. $9.8kJ$
• B. $2.8kJ$
• C. $0kJ$
• D. $12.8kJ$

Answer 1

Answer: (C)

$0kJ$

The correct answer is option().

$\Delta Q={\int }_{V_1}^{V_2}\left(\frac{\delta U}{\delta V}\right)dV$

From second law of thermodynamics

${\left(\frac{\delta U}{\delta V}\right)}_T=T{\left(\frac{\delta S}{\delta V}\right)}_T-p=T{\left(\frac{\delta p}{\delta T}\right)}_V-p,⟹p=\frac{RT}{v-b}-\frac{a}{V^2}⟹T{\left(\frac{\delta p}{\delta T}\right)}_V=\frac{RT}{v-b}or,{\left(\frac{\delta U}{\delta T}\right)}_T=\frac{a}{V^2}\Delta Q=a[\frac{1}{V_1}-\frac{1}{V_2}]=0kJ$