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During an experiment, an ideal gas is fo...

During an experiment, an ideal gas is found to obey an additional law `pV^(2)=constant`. The gas is initially at a temperature `T` and volume `V`. Find the temperature when it expands to a volume `2V`.

Text Solution

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According to the given problem `VP^(2)` =K. constant. So the gas equation PV = nRT in the light of above (eliminating P) yields
`((K)/(sqrt(V))) V = nRt , `i.e., `sqrt(V) = (nR)/(K ) T `
`therefore sqrt((V_(1))/(V_(2))) = ((T_(1))/(T_(2))), " i.e., " sqrt((V)/(2V)) = (T)/(T^(1))`
or `T^(1) = (sqrt(2))T `
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