Ncert Exercises & Solutions

Expansion of a gas in vacuum is called free expansion. Calculate the work done and the change in internal energy when 1L of ideal gas expands isothermally into vacuum until its total volume is 5L?

Work done of a gas in vacuum,

W = - p_{ext} (V_{2} - V_{1})

. As

p_{ext} = 0

W = - 0 (5 - 1) = 0

. As internal energy of an ideal gas depends only on temperature, therefore, for isothermal expansion of an ideal gas, internal energy remains constant.

i.e.,

∆ U = 0

It is to be remember that as

H = U + pV

∆ H = ∆ (U + pV) = ∆ U + p ∆ V = ∆ U + nR (∆ T)

. For isothermal process,

∆ T = 0

and also

∆ U = 0

, as stated above, therefore,

∆ H = 0

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