## Joule’s Law for a Perfect Gas

If a fixed mass of gas is allowed to expand without doing external work under the condition that no heat enters or leave the gas, i.e. the gas is allowed to undergo free expansion, then If the molecules of the gas attract one another, internal work will have to be done by the gas in pulling them apart and this will happen at the cost of internal kinetic energy of the gas which will therefore be cooled by the expansion.

On the other hand If the molecules repel one another the expansion should be accompanied by a rise in temperature and if there is no intermolecular attractions, then there should be no change in temperature.
Joule’s Experiment:-
Joule took two Copper cylinders A and B joined by a tube fitted with a stop cock. A contains air at high pressure while B is perfectly evacuated. Both cylinders were immersed in the minimum amount of water, whose tempreture was noted with a sensitive thermometer.
 Fig.  Joule’s apparatus
The stop cork was opened and air from cylinder A expanded into the cylinder B(vacum) and the expansion was so rapid that no heat communication was possible with the surrounding and hence a cooling was expected if intermolecular attractions exists

but Joule could not detect any change in tempreture.

Then he changes its experiment by emerging A and B in separate water baths but still no trace on intermolecular attractions was observed i.e. the fall of tempreture in A was exactly equal to rise in temperature of B.
If however intermolecular attractions existed then the fall in temperature in A would have been greater than the rise in temperature of B.
Hence Joule’s law stated that the Internal energy of a gas depends only on its temperature and is independent of its volume & pressure.

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