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The r.m.s. speed of gas at temperature $T$ is 2 times the r.m.s speed at $320 \mathrm{~K}$. The value of the Temperature $T$ is
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$1280 \mathrm{~K}$
According to the kinetic theory of gases the Kinetic energy of a molecule is proportional to the temperature.
$\begin{aligned} & \frac{K_1}{K_2}=\frac{T_1}{T_2}=\left(\frac{v_1}{v_2}\right)^2 \\ & \Rightarrow \frac{T_1}{320 \mathrm{~K}}=\left(\frac{2}{1}\right)^2 \\ & \Rightarrow T_1=1280 \mathrm{~K}\end{aligned}$
$\begin{aligned} & \frac{K_1}{K_2}=\frac{T_1}{T_2}=\left(\frac{v_1}{v_2}\right)^2 \\ & \Rightarrow \frac{T_1}{320 \mathrm{~K}}=\left(\frac{2}{1}\right)^2 \\ & \Rightarrow T_1=1280 \mathrm{~K}\end{aligned}$
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