• # question_answer One mole of an ideal monatomic gas is taken from temperature ${{T}_{0}}$ to $2{{T}_{0}}$ by the process$p{{T}^{4}}=C$.Considering the following statements. Choose the correct alternative. I. Molar heat capacity of the gas is $-\frac{3R}{2}$ II. Molar heat capacity of the gas is $\frac{3R}{2}$ III. Work done is $-3R{{T}_{0}}$ IV. Work done is 3 $R{{T}_{0}}$ A)  Statements I and IV are correct            B)  Statements I and III are correct C)  Statements II and IV are correct           D)  Statements II and III are correct

We have $p{{T}^{-4}}=C,\,\,\,p{{V}^{4/3}}=C$ $C=\frac{R}{\gamma -1}-\frac{R}{x-1}=\frac{3R}{2}-\frac{-3R}{2}$ $\left( \text{Here},\,\,\gamma =\frac{5}{3}\,\,\text{and}\,x=\frac{4}{3} \right)$ Now, $W=\frac{\eta R({{T}_{1}}-{{T}_{2}})}{\frac{4}{3}-1}=-3R{{T}_{0}}$