In the given pressure $(\mathrm{P})$ - absolute temperature $(\mathrm{T})$ graph of an ideal gas, the…

In the given pressure $(\mathrm{P})$ - absolute temperature $(\mathrm{T})$ graph of an ideal gas, the relation between volumes $V_1, V_2, V_3$ and $\mathrm{V}_4$ is
  1. $V_1=V_2=V_3=V_4$
  2. $V_1>V_2>V_3>V_4$
  3. $V_1>V_2>V_3 < V_4$
  4. $\mathrm{V}_1 < \mathrm{V}_2 < \mathrm{V}_3 < \mathrm{V}_4$

Solution

From the ideal gas equation $ \begin{aligned} & \mathrm{PV}=\mathrm{n} \cdot \mathrm{R} T \\ & \frac{\mathrm{P}}{\mathrm{T}}=\frac{\mathrm{C}}{\mathrm{V}} \\ & \mathrm{V}=\frac{\mathrm{C}}{\mathrm{P} / \mathrm{T}} \propto \frac{1}{\text { slop of the graph }} \end{aligned} $ Hence, $\mathrm{V}_1 < \mathrm{V}_2 < \mathrm{V}_3 < \mathrm{V}_4$

Asked in: AP EAMCET 2023 (19 May Shift 1)

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