Q157 / 200 · Manipal (MET) 2012 · Physics
A balloon contains $500 \mathrm{~m}^3$ of He at $27^{\circ} \mathrm{C}$ and 1 atmospheric pressure. The volume of He at $-3^{\circ} \mathrm{C}$ and 0.5 atmospheric pressure will be
- A$700 \mathrm{~m}^3$
- Correct answerB$900 \mathrm{~m}^3$
- C$1000 \mathrm{~m}^3$
- D$500 \mathrm{~m}^3$
Solution
Using standard gas equation,
$\begin{aligned}
\frac{p_1 V_1}{T_1} & =\frac{p_2 V_2}{T_2} \text { or } V_2=\frac{p_1 V_1 T_2}{p_2 T_1} \\
\therefore \quad & V_2=\frac{1 \times 500 \times(273-3)}{0.5 \times(273+27)} \\
& V_2=\frac{1 \times 500 \times 270}{0.5 \times 300} \\
& V_2=900 \mathrm{~m}^3
\end{aligned}$
Hence, the correct answer is option: 'B'.