Question

23. Challenge: A gas is heated so that it expands from a volume of 1.0L to a volume of 1.5 l. If the
initial temperature of the gas was 5.0°C, then what is the final temperature of the gas?

Answer 1

417 K is the “final temperature” of the gas.

Explanation:

According to “Charles law” the change in “volume” of a given mass of gas expanded is “directly proportional” to the “temperature” of the given gas expanded. When we keep “pressure” of the gas as constant. Mathematically,

$v \alpha T$

$\frac{v}{T}=\text { constant }$

If gas is expanded from initial volume to final volume and initial temperature to final temperature then,

$\frac{v_{1}}{T_{1}}=\frac{v_{2}}{T_{2}}$

$\begin{array}{l}{\text { Where, } v_{1} \text { and } v_{2} \text { are the initial and final volumes of the gas expanded recpectively,}} \\ {T_{1} \text { and } T_{2} \text { are the initial and final temperatures of the gas expanded recpectively }}\end{array}$

Given that,

Initial volume is 1.0L

Final volume is 1.5L

$\text { Initial temperatureis } 5.0^{\circ} \mathrm{C}=5+273=278 \mathrm{K}$

To find final temperature of the gas

Substitute the given values,

$\frac{1}{278}=\frac{1.5}{T_{2}}$

$T_{2}=1.5 \times 278$

$T_{2}=417 K$

Therefore, final temperature of the gas after expanding is 417 K.