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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

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a

$300 {Rlog}_{10} 2$

b

$81 {Rlog}_{e} 2$

c

$2 .3 \times 900 {Rlog}_{10} 2$

d

$900 {Rlog}_{10} 2$

answer is D.

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Detailed Solution

$\begin{array}{l} W = {μRTlog}_{e} \frac{V_{2}}{V_{1}} \\ = (\frac{m}{M}) {RTlog}_{e} \frac{V_{2}}{V_{1}} = 2 .3 \times \frac{m}{M} {RTlog}_{10} \frac{V_{2}}{V_{1}} \\ = 2 .3 \times \frac{96}{32} R (273 + 27) \log_{10} \frac{140}{70} = 2 .3 \times 900 {Rlog}_{10} 2 \end{array}$

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