Question

An ideal gas system undergoes an isothermal process, then the work done during the process is

• A. nRTln $\frac { V _ { 2 } } { V _ { 1 } }$
• B. nRTln
• C. 2nRTln $\frac { V _ { 2 } } { V _ { 1 } }$
• D. 2nRTln

Answer 1

Answer: (A)

nRTln $\frac { V _ { 2 } } { V _ { 1 } }$

Answer 2

: Let an ideal gas goes isothermally from its initial state $\left( P _ { 1 } V _ { 1 } \right)$ to the final state $\left( P _ { 2 } V _ { 2 } \right)$ then work done

$W = \int _ { V _ { 1 } } ^ { V _ { 2 } } P d V$

Taking $P V = n R T$ or $p = \frac { n R T } { V }$

Then, $W = \int _ { V _ { 1 } } ^ { V _ { 2 } } \frac { n R T } { V } d V = n R T \int _ { V _ { 1 } } ^ { V _ { 2 } } \frac { d V } { V } = n R T \ln \frac { V _ { 2 } } { V _ { 1 } }$