Question

One mole of oxygen gas is at a pressure of 5.60 atm and a temperature of 26.0°C. (a) If the gas is heated at constant volume until the pressure triples, what is the final temperature?
°C

(b) If the gas is heated so that both the pressure and volume are doubled, what is the final temperature?

Answer 1

Ideal gas equation is $pV=nRT$

(a)

since heating is at constant volume and the final pressure is triple the initial pressure, final temperature is triple the initial temperature.

$n=\frac{p_{1}V_{1}}{RT_{1}}=\frac{p_{2}V_{2}}{RT_{2}}$

constant volume $V_{1}=V_{2}$ and $3p_{1}=p_{2}$

$n=\frac{p_{1}V_{1}}{RT_{1}}=\frac{3p_{1}V_{1}}{RT_{2}}$

$T_{2}=3T_{1}=3(273+26)=3(299)=897\,K=624^{\circ}C$

(b)

since heating is such that the final pressure is double the initial pressure and final volume is double the initial volume, final temperature is four times the initial temperature.

$n=\frac{p_{1}V_{1}}{RT_{1}}=\frac{p_{2}V_{2}}{RT_{2}}$

$2V_{1}=V_{2}$ and $2p_{1}=p_{2}$

$n=\frac{p_{1}V_{1}}{RT_{1}}=\frac{2p_{1}\times2V_{1}}{RT_{2}}$

$T_{2}=4T_{1}=4(273+26)=4(299)=1196\,K=923^{\circ}C$