Temperature and Resistance..TPRH Sciences

[4563728]

In passage 38 for physics, #2 states: If the temperature of a piece of copper is lowered, the average random velocity of the free electrons will...
a. increase
b. decrease
c. remain the same
d. be reduced to zero

The answer is B and I understand their logical that temperature controls the movement of particles. But I was wondering doesn't resistance in a wire decrease with decreasing temperature? So due to a lack of resistance wouldn't the particle, experiencing less resistance from the wire, actually move faster?

Thank you in advance!

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[DrknoSDN]

http://www.sciencehq.com/physics/current-electricity.html (drift velocity)

"The speed of random motion is determined by temperature by,":
1/2mv^2 = 3/2KT
or
v = Root(3KT/m)

Where K is the boltzmann constant. 1.38x10^-23

So decreasing temperature decreases average random velocity. I would agree that uniform velocity would increase as long as their is a voltage difference to induce movement.

 

[neurodoc]

The question asks about the random velocity of free electrons. The Boltzman kinetic energy equation deals with the motion of gaseous particles of an "Ideal Gas," and it may or may not be applicable to free electrons in a copper conductor. Let's assume that the idea behind this equation applies to matter in general, in which case, yes, the random velocity of free electrons in a conductor would decrease with lower T. We just can't say that the average random velocity of such electrons will follow the ideal gas equation exactly, just that the velocity will be lower for lower temperatures.

OK, so what does that have to do with the conductor's electrical resistance? That was not in the question, but it is still an interesting question. One answer is that the resistance will decrease because the random motion decreases. Why? Perhaps because random free electron motion would be as likely to oppose the EMF induced electron motion as it would to facilitate it, the net effect of this is equivalent to mechanical friction in machines. Reducing the "friction" allows more useful work to be done, and in the case of electrical circuits this is achieved by lowering resistance.

 

[inasensegone]

In passage 38 for physics, #2 states: If the temperature of a piece of copper is lowered, the average random velocity of the free electrons will...
a. increase
b. decrease
c. remain the same
d. be reduced to zero

The answer is B and I understand their logical that temperature controls the movement of particles. But I was wondering doesn't resistance in a wire decrease with decreasing temperature? So due to a lack of resistance wouldn't the particle, experiencing less resistance from the wire, actually move faster?

Thank you in advance!

The above posters have presented some useful perspectives to answer your question, but let me give my 2 cents and hopefully give a more direct answer, MCAT-style.

The passage states: "The free electrons in a copper wire at room temperature are in constant thermal motion. They move in random directions...."
The passage later states: "The extra speed of the electrons due to the field is, in ordinary circuits, much smaller than their thermal speed."

Therefore it would stand to reason that if you lower the temperature, which has a greater effect on speed, then the average random velocity should decrease... even if the resistance also decreases. As DrknoSDN pointed out, they are explicitly asking about the average random velocity.... so even if the drift velocity which is opposite the electric field, increases, the overall average random velocity decreases. (current may very well increase in response to a decrease in resistance, but this does not exclude the observation that the average random velocity decreases... in fact it is in accordance with it).