Question

A container with insulating wall is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at pressure $P$ and temperature $T$, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be:

• A. $P,\frac{T}{2}$
• B. $\frac{P}{2},T$
• C. $\frac{P}{2},\frac{T}{2}$
• D. $P,T$

Answer 1

Answer: (B)

$\frac{P}{2},T$

$\text{Given:-}$ $P_1=P$ and $V_1=\frac{V}{2}$

$V_2=V$

$\text{Explanation:-}$

when value is opened, there will be free expansion of ideal gas, so temperature T remains constant. From Boyle's law

$P_1{V}_1=P_2{V}_2$

Here ,

$P_1=Pand{V}_1=\frac{V}{2}$

$V_2=V$

$\Rightarrow P_2=\frac{P_1{V}_2}{V_2}$

$=\frac{P\left(V/2\right)}{V}=\frac{P}{2}$

$\text{Hence the correct option is B}$