Question

An oxygen cylinder of volume $30$ litre has an initial gauge pressure of $15atm$ and a temperature of $27^{\circ }C$ After some oxygen is withdrawn from the cylinder, the gauge pressure drops to $11atm$ and its temperature drop to $17^{\circ }C$ Estimate the mass (in kg) of oxygen taken out of the cylinder, $R=8.3Jmo{l}^{-1}{K}^{-1}$, molecule weight of oxygen $=32$

Answer 1

Answer: 0.141

Given, $P_1=15+1$
= 16 atm (absolute)
$V_1=30\times 10^{-3}{m}^3$,
$T_1=273+27$
$=300K$
$P_2=12atm$,
$T_2=273+17$
$=290K$
We have $PV=\frac{m}{M}RT$
$\therefore m=\frac{P_{1}VM}{R{T}_1}$
$=\left[\frac{\left(16\times 1.013\times 10^5\right)\times \left(30\times 10^{-3}\right)\times \left(32\times 10^{-3}\right)}{8.31\times 300}\right]$
$=0.624kg$
Finally $m^{\prime }=\frac{P_{2}VM}{R{T}_2}$
$=\left[\frac{\left(12\times 1.013\times 10^5\right)\times \left(30\times 10^{-3}\right)\times \left(32\times 10^{-3}\right)}{8.31\times 290}\right]$
$=0.484kg$
The mass of the oxygen taken out $=m—m^{\prime }$
$=0.624-0.484$
$=0.141kg$