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A mass $m$ of a perfect gas at pressure $p_{1}$ and volume $V_{1}$ undergoes an isothermal process. The final pressure is $p_{2}$ and volume is $V_{2}$. The work done on the system is considered positive. If $R$ is the gas constant and $T$ is the temperature, then the work done in the process is 

  1. $p_{1}V_{1} \ln \dfrac{V_{2}}{V_{1}} \\$
  2. $-p_{1}V_{1} \ln\dfrac{P_{1}}{P_{2}} \\$
  3. $RT \ln \dfrac{V_{2}}{V_{1}} \\$
  4. $-mRT \ln \dfrac{P_{2}}{P_{1}}$
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