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  4. A balloon is filled at 27°C and 1 atm pressure by 50 m3 He. At -3°C and 0.5 atm pressure, the volume of He will be

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Q. A balloon is filled at $27^{\circ}C$ and $1$ atm pressure by $50\, m^3\,He$. At -$3^{\circ}C$ and $0.5$ atm pressure, the volume of $He$ will be

AIIMSAIIMS 2012

Solution:

$\frac{p_{1} V_{1}}{T_{1}}=\frac{p_{2} V_{2}}{T_{2}}$
or $V_{2}=\frac{p_{1} V_{1} T_{2}}{p_{2} T_{1}}$
$\therefore V_{2} =\frac{1 \times 500 \times(273-3)}{0.5 \times(273+27)} $
$V_{2} =\frac{1 \times 500 \times 270}{0.5 \times 300} $
$ V_{2} =900\, m ^{3} $