The temperature of a gas is - 50 ° C . To what temperature the gas should be heated so that the rms speed is…

RMS speed is given by, $v=\sqrt{\frac{3RT}{M}}$.

Therefore,

$v\propto \sqrt{T}$.

Given:

Initial temperature, $T_1=\left(-50+273\right) \mathrm{K}=223 \mathrm{K}$

Let, initial speed be $v$, then final speed will be $v+3v=4v$.

Now,

$$\begin{gathered} \frac{4v}{v}=\sqrt{\frac{T_2}{T_1}} \\ \Rightarrow T_2=16T_1 \\ =3568 \mathrm{K} \\ =\left(3568-273\right) °\mathrm{C} \\ =3295 °\mathrm{C} \end{gathered}$$