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  4. A vessel has 6 kg of hydrogen at pressure p and temperature 500 K . A small hole is made in it so, that hydrogen leaks out. How much hydrogen leaks out, if the final pressure is p/2 and temperature falls to 300 K?

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Q. A vessel has 6 kg of hydrogen at pressure p and temperature 500 K . A small hole is made in it so, that hydrogen leaks out. How much hydrogen leaks out, if the final pressure is p/2 and temperature falls to 300 K?

CMC MedicalCMC Medical 2014

Solution:

For ideal gas equation $ pV=\frac{m}{M}RT $ $ pV=\frac{6}{M}R\,(500) $ ?(i) Let x gram of hydrogen leaks out $ \frac{p}{2}V=\frac{(6-x)}{M}R\,(500) $ ...(ii) Dividing Eq. (ii) by Eq. (i), we have $ \frac{1}{2}=\frac{6-x}{6}-\frac{300}{500} $ $ \frac{1}{2}=\frac{6-x}{6} $ $ 6-x=5 $ $ x=1\,g $