The volume of a gas at $0^{\circ} \mathrm{C}$ is $2 \mathrm{dm}^3$. What is its volume if temperature is…

The volume of a gas at $0^{\circ} \mathrm{C}$ is $2 \mathrm{dm}^3$. What is its volume if temperature is decreased by $272^{\circ} \mathrm{C}$ ?
  1. $\left(\frac{3}{272}\right) \mathrm{dm}^3$
  2. $\left(\frac{2}{272}\right) \mathrm{dm}^3$
  3. $\left(\frac{4}{273}\right) \mathrm{dm}^3$
  4. $\left(\frac{2}{273}\right) \mathrm{dm}^3$

Solution

$\begin{aligned} & \mathrm{V}_1=2 \mathrm{dm}^3 \\ & \mathrm{~T}_1=273 \mathrm{~K} \\ & \mathrm{~T}_2=273-272=1 \mathrm{~K} \\ & \mathrm{~V}_2=? \\ & \frac{\mathrm{V}_1}{\mathrm{~T}_1}=\frac{\mathrm{V}_2}{\mathrm{~T}_2} \\ & \frac{2}{273}=\frac{\mathrm{V}_2}{1} \\ & \mathrm{~V}_2=\frac{2}{273} \mathrm{dm}^3\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 2)

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