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  4. The gas in a vessel is subjected to a pressure of 20 atm at a temperature 27°C. The pressure of the gas in a vessel after one-half of the gas is released from the vessel and the temperature of the remainder is raised by 50°C is

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Q. The gas in a vessel is subjected to a pressure of 20 atm at a temperature 27$^{\circ}$C. The pressure of the gas in a vessel after one-half of the gas is released from the vessel and the temperature of the remainder is raised by 50$^{\circ}$C is

Kinetic Theory

Solution:

Apply pV = $\mu RT = \frac{m}{M} RT$
$ \, \, \, \, \, \, \, \, \, \, \, \, \, 20 \times V = \frac{m}{M} \times R \times 300 \, \, \, \, \, \, \, \, \, \, \, \, \, ...(i)$
$\, \, \, \, \, \, \, \, \, \, p' \times V = \Bigg( \frac{ \frac{m}{2}}{M}\Bigg) R \times 350 \, \, \, \, \, \, \, \, \, \, \, \, \, ...(ii) $
From Eqs. (i) and (ii), we get
$p' = \frac{140}{12} \approx 11.7 \, atm$