Question

A gas is undergoing a change in state by an isothermal process AB as follows. Work done by gas in process AB is

• A. $100\ln 2Joule$
• B. $-100\ln 2Joule$
• C. $200\ln 2Joule$
• D. $-200\ln 2Joule$

Answer 1

The correct option is A

$100\ln 2Joule$

1. The isothermal process is a thermodynamic process in which the temperature T of a system remains constant $\left(T=0\right)$.
2. From the graph, it can be observed that pressure $P_1=1$, volume $V_1=100m^3,V_2=200m^3$
3. Work done in the isothermal process is calculated as follows: ${{\mathrm{W}}_{\mathrm{isothermal}}={\mathrm{P}}_1\mathrm{V}}_1\ln \frac{V_2}{V_1}$
4. Putting the values in the equation: $W_{isothermal}=1\times 100\ln \frac{200}{100}Joules$
5. Work done by the gas in process AB,${\mathit{W}}_{\mathbf{i}\mathbf{s}\mathbf{o}\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{r}\mathbf{m}\mathbf{a}\mathbf{l}}\mathbf{=}\mathbf{100}\mathbf{}\mathit{l}\mathit{n}\mathbf{2}\mathbf{}\mathit{J}$.
6. Hence, option A is correct.