AP EAMCET · PHYSICS · Kinetic Theory of Gases
The temperature at which the r.m.s velocity of a gas triples to its r.m.s. velocity at \(0^{\circ} \mathrm{C}\) is
- A \(2184 \mathrm{~K}\)
- B \(2184^{\circ} \mathrm{C}\)
- C \(2100^{\circ} \mathrm{C}\)
- D \(555 \mathrm{~J}\)
Answer & Solution
Correct Answer
(B) \(2184^{\circ} \mathrm{C}\)
Step-by-step Solution
Detailed explanation
For a gas, \(v_{\mathrm{rms}}=\sqrt{\frac{3 K T}{m}}\) or \(v_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}\) Here, \(T=\) Temperature in kelvin, Hence, \(\quad \frac{v_T}{v_0}=\sqrt{\frac{T}{0+273}}\) \(\Rightarrow\) Given, \(V_T=3 \times v_0\) so, \(\quad 3=\sqrt{\frac{T}{273}}\)…
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