First slide

Thermodynamic processes

Question

In an isothermal reversible expansion if the volume of 96gm oxygen at 27⁰C is increases from 70 liters to 140 liters, then the work done by the gas will be

Moderate

A

$300 R \log_{10}^{2}$
B

$81 R \log_{e}^{2}$
C

$900 R \log_{10}^{2}$
D

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

Solution

$\begin{array}{l} W = μ R T \log_{e} (\frac{V_{2}}{V_{1}}) \\ = \frac{m}{M} R T \log_{e} (\frac{V_{2}}{V_{1}}) = 2.3 \times \frac{m}{M} R T \log_{10} \frac{V_{2}}{V_{1}} \\ 2.3 \times \frac{96}{32} R (273 + 27) \log_{10} (\frac{140}{70}) \\ = 2.3 \times 900 R \log_{10} 2 \end{array}$

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