what temperature gives you double the rms speed?

Question

If the rms speed of the molecules in an ideal gas at 60°C increases by a factor of two, what is the new temperature?

From my notes and sites online, it says I can calculate rms speed by taking the square root of the temperature. And to double the speed, you'd have to quadruple the temperature. Ok I did that but 240 is not the answer (according to my homework site). So how should the new temperature be calculated?? I'm lost. help please! thanks

? · Accepted Answer

You have used the wrong temperature units.

Absolute temperature (i.e. in kelvin) is proportional to average kinetic energy.
Kinetic energy is proportional to speed².
Therefore absolute temperature is proportional to speed².

60°C = (60+273) = 333K

Since speed doubles, the temperature increase (2²=) 4 times to 4x333 = 1332K

You probably want the final answer in °C, so convert back:
T = (1332-273)°C  = 1059°C 

You may be expected to round the answer to 2 or 3 significant figures; if so, round to 1100°C  or 1060°C .

what temperature gives you double the rms speed?

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