TS EAMCET · Physics · Kinetic Theory of Gases
The temperature at which the rms speed of molecules in hydrogen gas will be double of its initial value at \(27^{\circ} \mathrm{C}\) is
- A \(300^{\circ} \mathrm{C}\)
- B \(1473^{\circ} \mathrm{C}\)
- C \(927^{\circ} \mathrm{C}\)
- D \(546^{\circ} \mathrm{C}\)
Answer & Solution
Correct Answer
(C) \(927^{\circ} \mathrm{C}\)
Step-by-step Solution
Detailed explanation
The rms speed of molecules in hydrogen gas is \[ v_{\mathrm{rms}}=\sqrt{\frac{3 k_B T}{m}} \] where, \(m=\) mass of hydrogen, \(k_B=\) Boltzmann's constant and \(T=\) temperature in kelvin. \[ \therefore \quad v_{\text {rms }} \propto \sqrt{T} \] Initial temperature,…
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