Answer to Question #260416 in Physics for Boss

Question

At what temperature will the molecule of an ideal gas have twice the the rms speed they have at 20°c

Answer 1

The speed is proportional to the square root of temperature:

$v_\text{rms}=\sqrt\frac{3RT}{M},\\\space\\ u=2v_\text{rms}=2\sqrt\frac{3RT}{M}=\sqrt\frac{3R(4T)}{M},$

so, the temperature is 4T=4(273+20)=1172 K or 899°C.