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  4. A gas at a pressure of 5.0 atm is heated from 0° to 546° C and simultaneously compressed to one-third of its original volume. Hence final pressure is

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Q. A gas at a pressure of $5.0\, atm$ is heated from $0^{\circ}$ to $546^{\circ} C$ and simultaneously compressed to one-third of its original volume. Hence final pressure is

States of Matter

Solution:

$P_{1}=5.0\,atm$ , $T_{1}=0^{\circ}C=273\,K, V_{1}=V$
$P_{2}$ =? $T_{2}=546^{\circ}C=819\,K, V_{2}=\frac{1}{3} V $
$\therefore $ From $\frac{P_{1} V_{1}}{P_{2} V_{2}}=\frac{T_{1}}{T_{2}}$
$\Rightarrow \frac{5\times V}{P_{2}\times\frac{1}{3}V}=\frac{273}{819}$
$\Rightarrow \frac{5\times3}{P_{2}}=\frac{1}{3}$
$\Rightarrow P_{2}=45 \,atm$