A container is filled with a gas at a temperature of 299 K such that its pressur
ID: 1473570 • Letter: A
Question
A container is filled with a gas at a temperature of 299 K such that its pressure is 2.30 105 Pa.
(a) If the average kinetic energy of a molecule in the gas is to be quintupled, by what factor must the rms speed decrease or increase?
=
State whether the rms speed decreases or increases.
decreasesincreases
(b) If the average kinetic energy of a molecule in the gas is to be halved, by what factor must the rms speed decrease or increase?
=
State whether the rms speed decreases or increases.
decreasesincreases
vrms,f vrms,iExplanation / Answer
the average kinetic energy of a molecule is,
Kavg = 0.5mvrms,i2
if Kavg = 5Kavg, then the above equation becomes as,
5Kavg = 0.5mvrms,f2
the ratio vrms,f/vrms,i is,
vrms,f/vrms,i = sqrt[5] = 2.236, increases
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if Kavg = 0.5Kavg, then the ratio vrms,f/vrms,i is,
vrms,f/vrms,i = sqrt[0.5] = 0.707, decreases
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