Correct Answer - Option 1 : 819°C

__CONCEPT:__

**Root mean square (R.M.S.) velocity.**

- we know how to relate temperature and kinetic energy, we can relate temperature to the velocity of gas molecules. Note since these are distributions the values (E
_{k} or velocity) that we are talking about are always averages

\(E_k = \frac{3}{2}RT\)

\(E_k = \frac{1}{2}mv^{2}\)

- setting these two equal and solving for the average square velocity we get.

\(v^{2} = \frac{3RT}{m}\)

- The root mean square velocity or V
_{rms} is the square root of the average square velocity and is

\(R.M.S = \sqrt{\frac{3RT}{M}}\)

where** R = gas constant**, **T = temperature** (in K), **M = molar mass of the gas**

******EXPLANATIONS:**

- From the gas equation, we know

\(c = \sqrt{\frac{3RT}{m}}\)

\(\frac{C_T}{C_o}= \sqrt{\frac{T}{T_o}} => \frac{2C_o}{C_o} = \sqrt{\frac{T}{T_o}}\)

\(=> 4 = \frac{T}{T_o}\)

\(=>T = 4T_o = 4 \times 273 = 1092K = 819^0 C\)

- hence option 1 is the correct answer.