Q. The gas in vessel is subjected to a pressure of 20 atmosphere at a temperature $27℃.$ 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 $50℃$ is
A) $8.5\ atm$
B) $10.8\ atm$
C) $11.7\ atm$
D) $17\ atm$
Explanation
(c) $PV = \mu RT = \frac{m}{M}RT \Rightarrow P \propto mT$
$\Rightarrow \frac{P_{2}}{P_{1}} = \frac{m_{2}}{m_{1}}\frac{T_{2}}{T_{1}} = \frac{1}{2} \times \frac{(273 + 27 + 50)}{(273 + 27)} = \frac{7}{12}$
$\Rightarrow P_{2} = \frac{7}{12}P_{1} = \frac{7}{12} \times 20 = 11.67atm.\ \approx 11.7atm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.