Q. 50

# 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 amount of work done by the gas. If the same expansion were carried out reversibly, will the work done be higher or lower than the earlier case? (Given that 1 L bar = 100 J)

o For the first case, this is an irreversible expansion of the ideal gas occurs, hence the amount of work done = -pext ∆V

= - 2 bar × (50 – 10 ) L = - 80 L bar.

Now, it is given that 1 L bar = 100 J

So , -80 L bar = (-80 × 100) = -8000 J = -8 KJ is the amount of work done in the above process.

o If the same expansion were carried out reversibly, (i.e. through infinite steps) then the internal pressure of the gas will be infinitesimally larger than the external pressure and this will be the case in every stage of expansion. Therefore, the work done will own a higher value than the earlier case.

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