Question

The gas in a vessel in subjected to a pressure of $20$ atmosphere at a temperature ${27}^{\circ }C$. The pressure of the gas in the 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

• A. $8.5atm$
• B. $10.8atm$
• C. $11.7atm$
• D. $17atm$

Answer 1

The correct option is C $11.7atm$

From ideal gas equation we get, $PV=\frac{m}{M}RT$
Initial conditions : $P=20atm$ $T=27+273=300K$
$20\times V=\frac{m}{M}R\times 300$
Final conditions : $T^{\prime }=300+50=350K$, $m^{\prime }=\frac{m}{2}$
$P^{\prime }\times V=\frac{\left(m/2\right)}{M}R\times 350$
$\therefore$ $\frac{P^{\prime }}{20}=\frac{350}{2\times 300}$
$\therefore P^{\prime }=11.7atm$.