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In a cylinder...

Question

In a cylinder , $2$ mole of an ideal gas at temperature $300 k$ undergoes isothermal expansion until its volume double. Work done by the gas is $l o g_{e} 2 = 0.693)$

A

1875 J

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B

2695 J

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C

3457 J

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D

4485 J

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Solution

The correct option is C $3457 J$
In isothermal expansion, T is constant
$P V = n R T =$ constant
$∴ P_{1} V_{1} = P_{2} V_{2} = K$ , $P = \frac{K}{V}$
Workdone $= \int P d v = \int \frac{K}{V} d c$
$= k l o g_{e} \frac{v_{2}}{v_{1}} = k l o g_{e} \frac{2 v}{v} = k l o g_{e} 2$
Also, $k = n R T = 2 \times R \times 300 = 600 R$
$∴$ Work done $= 600 R l o g_{e} 2 = 3456.9612$
$= 3.456$ kJ.

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