TS EAMCET · Physics · Kinetic Theory of Gases
The temperature at which the rms speed of oxygen molecules is \(75 \%\) of rms speed of nitrogen molecules at a temperature of \(287^{\circ} \mathrm{C}\) is
- A \(87^{\circ} \mathrm{C}\)
- B \(127^{\circ} \mathrm{C}\)
- C \(227^{\circ} \mathrm{C}\)
- D \(360^{\circ} \mathrm{C}\)
Answer & Solution
Correct Answer
(A) \(87^{\circ} \mathrm{C}\)
Step-by-step Solution
Detailed explanation
\(R M S\) speed, \(v_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}} \Rightarrow v_{\mathrm{rms}} \propto \sqrt{\frac{\mathrm{T}}{\mathrm{M}}}\) \(\mathrm{v}_{\mathrm{rms}, \mathrm{o}}=75 \%\) of \(\mathrm{v}_{\mathrm{rms}, \mathrm{N}}=\frac{3}{4} \mathrm{v}_{\mathrm{rms}, \mathrm{N}}\)…
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