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Q.
A certain mass of gas occupies a volume of 300 cc at $27\text{℃}$ and 620 mm pressure. The volume of this gas at $47\text{℃}$ and 640 mm pressure will be
NTA AbhyasNTA Abhyas 2022
Solution:
Given initial volume $\left(\left(\text{V}\right)_{1}\right)=300 \, \text{c}\text{c};$ initial temperature $\left(\left(\text{T}\right)_{1}\right)=27\text{℃}=300 \, \text{K},$ initial pressure $\left(\left(\text{p}\right)_{1}\right)=620 \, \text{m}\text{m},$ final temperature $\left(\left(\text{T}\right)_{2}\right)=47\text{℃}=320 \, \text{K}$ and final pressure $\left(\left(\text{p}\right)_{2}\right)=640 \, \text{m}\text{m}.$ We know from the general gas equation
$\frac{\text{p}_{1} \text{V}_{1}}{\text{T}_{1}}=\frac{\text{p}_{2} \text{V}_{2}}{\text{T}_{2}}$
$\Rightarrow \frac{620 \times 300}{300}=\frac{640 \times \text{V}_{2}}{320}$
$\Rightarrow 310CC$
$\left(\text{w} \text{h} \text{e} \text{r} \text{e} , \, \left(\text{V}\right)_{2} \, \text{i} \text{s} \, \text{t} \text{h} \text{e} \, \text{f} \text{i} \text{n} \text{a} \text{l} \, \text{v} \text{o} \text{l} \text{u} \text{m} \text{e} \, \text{o} \text{f} \, \text{t} \text{h} \text{e} \, \text{g} \text{a} \text{s}\right)$