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  • In an isothermal reversible expansion, if the volume of 96 gm of oxygen at 27°C is increased from 70 litres to 140 litres, then the work done by the gas will be</s

In an isothermal reversible expansion, if the volume of 96 gm of oxygen at 27°C is increased from 70 litres to 140 litres, then the work done by the gas will be

Option: 1

300.R.log_{10}2

 


Option: 2

80.R.log_{e}2


Option: 3

900.R.log_{10}2


Option: 4

2.3 \times 900.R.log_{10}2


Answers (1)

best_answer

 

 

 

 

The formula of Work done in the isothermal process - 

\begin{array}{l}{W=n R T \log _{e}\left(\frac{V_{f}}{V_{i}}\right)=2.303n R T \log _{10}\left(\frac{V_{f}}{V_{i}}\right)} \\ {W=n R T \log _{e}\left(\frac{P_{i}}{P_{f}}\right)=2.303 nR T \log _{10}\left(\frac{P_{i}}{P_{f}}\right)}\end{array}

 

\\ \\ \\ \begin{aligned} W &=\mu R T \log _{e} \frac{V_{2}}{V_{1}} |=\left(\frac{m}{M}\right) R T \log _{e} \frac{V_{2}}{V_{1}}=2.3 \times \frac{m}{M} R T \log _{10} \frac{V_{2}}{V_{1}} \\=2.3 \times \frac{96}{32} R(273+27) \log _{10} \frac{140}{70} &=2.3 \times 900 R \log _{10} 2 \end{aligned}

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rishi.raj

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