KCET · Physics · Kinetic Theory of Gases
The temperature of a gas contained in a closed vessel of constant volume increases by \(1^{\circ} \mathrm{C}\) when the pressure of the gas is increased by \(1 \%\). The initial temperature of the gas is
- A \(100 \mathrm{~K}\)
- B \(273^{\circ} \mathrm{C}\)
- C \(100^{\circ} \mathrm{C}\)
- D \(200 \mathrm{~K}\)
Answer & Solution
Correct Answer
(A) \(100 \mathrm{~K}\)
Step-by-step Solution
Detailed explanation
According to Gay Lussac's law \(\mathrm{p} \propto \mathrm{T}\)
\(\therefore \frac{\mathrm{dp}}{\mathrm{p}} \times 100=\frac{\mathrm{dT}}{\mathrm{T}} \times 100 \)
\(1 =\frac{1}{\mathrm{~T}} \times 100 \)
\(\Rightarrow \mathrm{T}=100 \mathrm{~K}\)
\(\therefore \frac{\mathrm{dp}}{\mathrm{p}} \times 100=\frac{\mathrm{dT}}{\mathrm{T}} \times 100 \)
\(1 =\frac{1}{\mathrm{~T}} \times 100 \)
\(\Rightarrow \mathrm{T}=100 \mathrm{~K}\)
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