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?

If speed increases by 3 times, fi nal speed will be 4 times

We know $V_{\mathrm{rms}}=\sqrt{\frac{3RT}{M}}$

$\frac{V_1}{V_2}=\sqrt{\frac{T_1}{T_2}}$

$\frac{V_1}{4V_1}=\sqrt{\frac{T_1}{T_2}}$

T₂ = 16   T₁ = 16 ( 273-50) = 3568 K
T₂ = 3568 -273 = 3295°C