A certain gas is at a temperature of 350 K. If the temperature is raised to 700 K, the average translational kinetic energy of the gas will increase by

Expression of average translational kinetic energy is:

${\mathrm{KE}}_{\text{avg }}\left(\text{ translational }\right)=\frac{3}{2}KT$

K is constant, which means that average translational kinetic energy is proportional to the temperature of the gas.

Assume that initial temperature (T_i) is 350 K and its K.E. is x. If final temperature (T_f) is 700 K, then its K.E. is increases by:

$$\begin{gathered} \frac{{\left(\mathrm{K}.\mathrm{E}.\right)}_{\mathrm{i}}}{{\left(\mathrm{K}.\mathrm{E}.\right)}_{\mathrm{f}}}=\frac{{\mathrm{T}}_{\mathrm{i}}}{{\mathrm{T}}_{\mathrm{f}}} \\ \frac{\mathrm{x}}{{\left(\mathrm{K}.\mathrm{E}.\right)}_{\mathrm{f}}}=\frac{350 \mathrm{K}}{700 \mathrm{K}} \\ {\left(\mathrm{K}.\mathrm{E}.\right)}_{\mathrm{f}}=\frac{700 \mathrm{K}\times \mathrm{x}}{350 \mathrm{K}}=2\mathrm{x} \end{gathered}$$