A hot air balloon has volume of $2000 \mathrm{dm}^3$ at $99^{\circ} \mathrm{C}$. What is the new volume if…

A hot air balloon has volume of $2000 \mathrm{dm}^3$ at $99^{\circ} \mathrm{C}$. What is the new volume if air in balloon cools to $80^{\circ} \mathrm{C}$ ?
  1. $2428.9 \mathrm{dm}^3$
  2. $2656.9 \mathrm{dm}^3$
  3. $2814.9 \mathrm{dm}^3$
  4. $1897.8 \mathrm{dm}^3$

Solution

$\begin{array}{ll} & \text { Using Charles' law, } \\ & \frac{\mathrm{V}_1}{\mathrm{~T}_1}=\frac{\mathrm{V}_2}{\mathrm{~T}_2} \\ \therefore \quad & \frac{2000 \mathrm{dm}^3}{372 \mathrm{~K}}=\frac{\mathrm{V}_2}{353 \mathrm{~K}} \\ \therefore \quad & \mathrm{V}_2=\frac{2000 \times 353}{372}=1897.8 \mathrm{dm}^3\end{array}$

Asked in: MHT CET 2023 (12 May Shift 1)

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