Question

Consider a mole of a monoatomic gas which occupies a volume of $100c.c$ . at $36mm$ pressure. If the volume occupied by $5$ moles of gas at one-third of the initial pressure and at a one-ninth of the initial temperature will be $\frac{V}{3}mL$ . Find $V.$ (approximate to two decimals).

Answer 1

Equation of state is given by,
$PV=nRT$
$\therefore \frac{P V}{n T}=$ constant
$\therefore \frac{P_{1} V_{1}}{n_{1} T_{1}}=\frac{P_{2} V_{2}}{n_{2} T_{2}}$
$\therefore \frac{36 \times 100}{1 \times T_{1}}=\frac{12 V_{2} \times 9}{5 \times T_{1}}$
$\therefore V_{2}=\frac{36 \times 100 \times 5}{12 \times 9}=\frac{500}{3}c.c.$
$1c.c.=1mL$