Question

A cylindrical container of volume 44.8 litres is containing equal no, of moles (in integer no) of an ideal monoatomic gas in two sections A and B separated by an adiabatic frictionless piston as shown in figure. The initial temperature and pressure of gas in both section is 27.3 K and 1 atm. Now gas in section A is slowly heated till the volume of section B becomes ${\left(1/8\right)}^{th}$ of initial volume.
Given : R=2 cal.mol-K, $C_{vm}$ of monoatomic gas = $\frac{3}{2}R$,
At 1 atm $0$ ideal gas occupy 22.4 litre.
What will be the final pressure in container B :

• A. 2 atm
• B. 8 atm
• C. 16 atm
• D. 32 atm

Answer 1

The correct option is B 8 atm

$\begin{array}{c}T=27.3KP=1\text{atm}\\ \text{In container}B\\ V_f=V/8V_i=PV=c\text{onst.}\\ 1\times {\left(\frac{V_i}{V_f}\right)}^{5/3}{P}_{fr}=5/3\\ P_f=(8{)}^{5/3}=32\text{atm}\end{array}$

$\begin{array}{c}\text{In container}A,V_f=22.4+\frac{7}{8}\times 22.5\\ =\frac{15}{8}\times 22.5\\ V_f=\frac{15}{8}{V}_i\\ \therefore P_f=8atm\end{array}$