fosilifer0ag

2023-03-14

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

unieventos8l9

Work done in vacuum is calculated by:
$w=-{P}_{\text{ext}}\left({V}_{\text{final}}-{V}_{\text{initial}}\right)$
For the given problem: ${P}_{\text{ext}}=0$, because it is a free expansion (in the vacuum).
Hence,
$w=-\left(0×\left(5-1\right)\right)\phantom{\rule{0ex}{0ex}}w=0$
According to joule experimental observation, For an isothermal expansion of ideal gas, no heat will be absorbed or evolved, hence q=0.
By the 1st law of thermodynamics,
$q+w=\mathrm{△}U\phantom{\rule{0ex}{0ex}}\mathrm{△}U=0$
Since, w=0 and q=0, then the change in internal energy $\mathrm{△}U$ will also be 0.

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