Two moles of an ideal gas is expanded to double its volume by two different processes. One is isobaric and the other one is isothermal. If W1 and W2 are the work done respectively, then

Two moles of an ideal gas is expanded to double its volume by two different processes. One is isobaric and the other one is isothermal. If W₁ and W₂ are the work done respectively, then

A
$\frac{W_{1}}{W_{2}} = 0 .693$
B
$\frac{W_{1}}{W_{2}} = 1 .443$
C
$W_{1} = W_{2}$
D
$W_{1} = 0.325$

Solution:

$W_{1} = p_{1} (v_{2} - v_{1}) = p_{1} (2 v_{1} - v_{1}) = p_{1} v_{1}$

$W_{2} = p_{1} v_{1} \ln (\frac{v_{2}}{v_{1}}) = p_{1} v_{1} \ln 2 = p_{1} v_{1} \times 0.693$

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