Question:
During an experiment, an ideal gas is found to obey an additional law \(Vp^2 = \text{constant}\). The gas is initially at temperature \(T\) and volume \(V\). The temperature of the gas when it expands to a volume \(2V\) is:
During an experiment, an ideal gas is found to obey an additional law \(Vp^2 = \text{constant}\). The gas is initially at temperature \(T\) and volume \(V\). The temperature of the gas when it expands to a volume \(2V\) is:
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When given a non-standard relation, express one variable in terms of another and substitute into \(pV=nRT\).
Updated On: Jun 16, 2026
- \(2T\)
- \(4T\)
- \(6T\)
- \(5T\)
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The Correct Option is A
Solution and Explanation
Concept: \[ V p^2 = \text{constant}, \quad pV = nRT \]
Step 1: \[ V p^2 = k \Rightarrow p^2 \propto \frac{1}{V} \Rightarrow p \propto \frac{1}{\sqrt{V}} \]
Step 2: \[ T \propto pV \Rightarrow T \propto \frac{V}{\sqrt{V}} = \sqrt{V} \]
Step 3: \[ \frac{T'}{T} = \sqrt{\frac{2V}{V}} = \sqrt{2} \] \[ T' = T\sqrt{2} \] Since \(\sqrt{2} \approx 1.414\), closest option is \(2T\).
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