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:

• A. \(2T\)
• B. \(4T\)
• C. \(6T\)
• D. \(5T\)

Hint:

When given a non-standard relation, express one variable in terms of another and substitute into \(pV=nRT\).

Answer 1

The Correct Option is A

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 \(2T\).