Heat and Thermodynamics 4 Question 24
26. A vessel contains 1 mole of $O _2$ gas (molar mass 32) at a temperature $T$. The pressure of the gas is $p$. An identical vessel containing one mole of the gas (molar mass 4) at a temperature $2 T$ has a pressure of
(1997, 1M)
(a) $p / 8$
(b) $p$
(c) $2 p$
(d) $8 p$
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Solution:
$$ \begin{aligned} p V & =n R T \\ p & =\frac{n R T}{V} \quad \text { or } \quad p \propto T \end{aligned} $$
or
if $V$ and $n$ are same. Therefore, if $T$ is doubled, pressure also becomes two times i.e. $2 p$.
