MHT CET · Physics · Thermodynamics
A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is (Molecular wt. of \(\mathrm{O}_2 \& \mathrm{H}_2\) is 32 and 2 respectively)
- A \(1: 4\)
- B \(1: 8\)
- C \(16: 1\)
- D \(12: 1\)
Answer & Solution
Correct Answer
(C) \(16: 1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& \mathrm{P}_1 \mathrm{~V}_1=\frac{\mathrm{m}_1}{\mathrm{M}_1} \mathrm{RT}_1 \\
& \mathrm{P}_2 \mathrm{~V}_2=\frac{\mathrm{m}_2}{\mathrm{M}_2} \mathrm{RT}_2
\end{aligned}\)
Dividing (i) by (ii)
\(\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{\mathrm{M}_1}{\mathrm{M}_2}=\frac{32}{2}=\frac{16}{1}\)
& \mathrm{P}_1 \mathrm{~V}_1=\frac{\mathrm{m}_1}{\mathrm{M}_1} \mathrm{RT}_1 \\
& \mathrm{P}_2 \mathrm{~V}_2=\frac{\mathrm{m}_2}{\mathrm{M}_2} \mathrm{RT}_2
\end{aligned}\)
Dividing (i) by (ii)
\(\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{\mathrm{M}_1}{\mathrm{M}_2}=\frac{32}{2}=\frac{16}{1}\)
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