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W work is done in expanding a gas to double its volume by isobaric process and w’ is work done in expanding this gas to double its volume by isothermal process from the same state. Then W/w’ is

W work is done in expanding a gas to double its volume by isobaric process and w’ is work done in expanding this gas to double its volume by isothermal process from the same state. Then W/w’ is

Grade:11

1 Answers

Kruthik
119 Points
6 years ago
I think 1/loge2 is the answer. Let’s see how.
Let Pi,Ti, and Vo be the initial pressure, temperature, and volume.
Consider the isobaric expansion.
Work done in isobaric expansion is PΔV, so W=Pi(2Vo – Vo). = Pi(Vo).
Now let’s consider the isothermal expansion.
Work done in isothermal process is given by, W = nRTloge(Vi/Vf).
So, W’ = nRTiloge(2Vo/Vo) = nRTiloge2.
By ideal gas law, nRTi = PiVo.
Thus, W’=PiVologe2.
Hence, W/W’ = 1/loge2.
 

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