MHT CET · Physics · Kinetic Theory of Gases
The r.m.s. velocity of gas molecules kept at temperature \(27^{\circ} \mathrm{C}\) in a vessel is \(61 \mathrm{~m} / \mathrm{s}\). Molecular weight of gas is nearly
\(\left[\mathrm{R}=8.31 \frac{\mathrm{~J}}{\mathrm{~mol} \mathrm{~K}}\right]\)
- A 2
- B 28
- C 4
- D 32
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
Given,
\(T=27^{\circ} \mathrm{C}+273=300 \mathrm{~K} \)
Also, \(v_{\mathrm{rms}}=61 \mathrm{~m} / \mathrm{s} \)
\( \mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}} \)
\( \therefore M=\frac{3 R T}{\mathrm{v}_{\mathrm{ms}}^2}=\frac{3 \times 8.31 \times 300}{61 \times 61}=2\)
\(T=27^{\circ} \mathrm{C}+273=300 \mathrm{~K} \)
Also, \(v_{\mathrm{rms}}=61 \mathrm{~m} / \mathrm{s} \)
\( \mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}} \)
\( \therefore M=\frac{3 R T}{\mathrm{v}_{\mathrm{ms}}^2}=\frac{3 \times 8.31 \times 300}{61 \times 61}=2\)
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