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Question
An ideal gas is allowed to expand against a constant pressure of 2 bar from 10 L to 50 L in one step. Calculate the magnitude of work done by the gas. If the same expansion were carried out reversibly, will the magnitude work done be higher or lower than the earlier case? (Given that, 1 L bar=100 J)
An ideal gas is allowed to expand against a constant pressure of 2 bar from 10 L to 50 L in one step. Calculate the magnitude of work done by the gas. If the same expansion were carried out reversibly, will the magnitude work done be higher or lower than the earlier case? (Given that, 1 L bar=100 J)
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Solution
The correct option is B −8 kJ , higher
In the first case, as the expansion is against a constant external pressure, work done is given as
w = −Pext(V2−V1)
Pext=2 bar
V1=10 L
V2=50 L
w=−2 bar×(50−10) L
=−80 L bar
Since, 1 L bar=100 J
w=−80×100 J =−8kJ
(-ve sign shows work is done by the system)
If the above expansion were carried out reversibly, the internal pressure of the gas should be infinetisimally greater than the external pressure at every stage. Hence, the work done will be more.
In the first case, as the expansion is against a constant external pressure, work done is given as
w = −Pext(V2−V1)
Pext=2 bar
V1=10 L
V2=50 L
w=−2 bar×(50−10) L
=−80 L bar
Since, 1 L bar=100 J
w=−80×100 J =−8kJ
(-ve sign shows work is done by the system)
If the above expansion were carried out reversibly, the internal pressure of the gas should be infinetisimally greater than the external pressure at every stage. Hence, the work done will be more.
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