One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is ______ J (nearest integer) [2023]

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Solution

Q.
One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is ______ J (nearest integer) [2023]

Given: log 2 = 0.3
ln 10 = 2.3

Ans.
(620)

$W_{1 \to 2} = - 1 (40 - 20) = -20 bar lit.$

$W_{2 \to 3} = 0$

$W_{3 \to 1} = - n R T \ln (\frac{V_{2}}{V_{1}})$

$= - P_{1} V_{1} \ln (\frac{V_{2}}{V_{1}})$

$= - 1 \times 20 ln \frac{20}{40}$

$= 20 ln 2$

$= 20 \times 2.3 \times 0.3 = 13.8 bar lit.$

$W_{total} = - 20 + 13.8$

$= - 6.2 bar lit. (1 bar lit.=100 J)$

$W_{total} = - 6.2 \times 100 = -620 J$

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