Question

A bulb of unknown volume V contains a gas at $1$ atm pressure. This bulb was connected to another evacuated bulb of volume $0.5$L through a stop cock. When the stop cock was opened, the pressure at each bulb becomes $7.58\times {10}^4$ Pa mm while the temperature remained constant. Calculate V in litres.

Answer 1

From ideal gas equation,

$PV=nRT$

At constant temperature,

$PV=\text{constant}$

$\Rightarrow P_1{V}_1=P_2{V}_2.....\left(1\right)$

Given:-

Pressure of first bulb $\left(P_1\right)=1atm=1.013\times {10}^{5}Pa$

Volume of first bulb $\left(V_1\right)=V$

After opening the stop cock,

Total pressure $\left(P_2\right)=7.58\times {10}^{4}Pa$

Total volume $\left(V_2\right)=(V+0.5)L$

Now from ${eq}^n\left(1\right)$, we have

$1.01\times {10}^5\times V=7.58\times {10}^4\times (V+0.5)$

$\Rightarrow 10V=7.5V+3.75$

$\Rightarrow 2.5V=3.75$

$\Rightarrow V=1.5L$

Hence the volume of the bulb is $1.5L$.