The temperature of a gas is −50°C. To what temperature the gas should be heated so that the rms speed is increased by 3 times?
Answer & explanation
Correct answer: option 3
$ V_{rms} \propto \sqrt{T} $
Its velocity increases by three times
$\Rightarrow \Delta V = 3V_1 , V_2 - V_1 = 3V_1, V_2 = V_1 + 3V_1 = 4V_1$
$\Rightarrow \frac{V_2}{V_1} = 4 =\sqrt {\frac{T_2}{T_1}}$
$ T_2 = 16 T_1 = 16 \times (273-50)K = 3568nK = (3568 - 273)^oC = 3295^oC$