A vessel contains 8 gm of air at 400 K. Some amount of air leaks out through a hole provided to it. After some time, the pressure is halved and the temperature is changed to 300 K. Find the mass of air escaped.

A vessel contains 8 gm of air at 400 K. Some amount of air leaks out t

1.	A vessel contains 8 gm of air at 400 K. Some amount of air leaks out through a hole provided to it. After some time, the pressure is halved and the temperature is changed to 300 K. Find the mass of air escaped.
Answer» <P> Solution :Initial of the air `(m_(1))=8gm` , Initial TEMPERATURE `(T_(1))=400K`, Initial pressure of the air `(P_(1))=P` Final mass of the air `=m_(2)`, Final temperature `(T_(2))=300K` Final pressure of the air `(P_(2))=P//2` From the GAS equation, `P_(1)/(m_(1)T_(1))=P_(2)/(m_(2)T_(2)) rArr m_(2)=P_(2)/P_(1) TIMES T_(1)/T_(2) times m_(1)=(P//2)/P times 400/300 times 8=1/2 times 4/3 times 8=16/3=5.33` `therefore m_(2)=5.33` GM, Mass of the gas escaped `=m_(1)-m_(2)=8-5.33=2.67gm`