You have a sample of gas at 0 C. You wish to increase the
rms spe...

Question

You have a sample of gas at 0 C. You wish to increase the
rms speed by a factor of 3. To what temperature should
the gas be heated?

Accepted Answer

Hi everyone here we have a question telling us initially a gas is at 300 kelvin determine the temperature required to increase the B R M. S by a factor of four. So r V R M. S final Is going to equal four times VRM. S. initial. And now we can plug in our formula for V R M. S. So we get three times r. Gas constant times our temperature over our molar mass equals four times the square root of three times r gas constant times our temperature initial over molar mass. So we're going to square each side to get rid of our square root and that's going to give us three R. T. Over in Equals 16 because we're squaring our four Times three R. T. Over in. And now we're going to Multiply both sides by three or we're going to multiply by three. We're gonna multiply our 16 by three. So that gives us three R. T over. N equals 48. Our Times 300 Kelvin. And now we're going to divide both sides by three. So we get our T over M equals 16. Our Times 300 Kelvin over. Em and we can cancel out our ours and our ems. So then we get temperature Equal 16 times 300 Kelvin Which equals 4800 Kelvin. And that is our final answer. Thank you for watching. Bye

Watch next