in a vacuum, the relationship between the rate of cooling and temperature is.?

Question

a.cooling is proportional to temperature.
b. cooling is proportional to the square root of temerpature.
c. cooling is proportional to the square of temperature.
d. cooling is proportional to the fourth power of temperature.
e. cooling is proportional to temperature to the power one quarter.

Answer 1

If you consider this heat transfer as conduction, then the equation your looking for is ....

dQ/dt = -KA * dT/dx

> where Q is heat being transfered
> t is time
> dQ/dt is heat flux. ie amount of heat being transfered per time ie rate of heat transfer.
> -K is a constant and the negative sign gives direction of heat flow
> A is cross sectional area of heat transfer area
> T is temp. so dT is change in temp between hot and cold
> x is distance between hot and cold

for constant area and for constant "x" if you only want to consider the relationship between dQ/dt and T, then ....

dQ/dt is proportional to dT and your answer is (a)

********update***********

firebird. you can transfer heat between two objects via conduction in a vacuum. imagine a cold object in contact with a hot object inside of a vacuum.

of course if you want to consider radiation, then the equation is

dQ/dt = d(k' x T^4)/dt

in which case (d) would be the answer.

so, both (a) and (d) are defendable answers.


***** another update ****

hummm. three thumbs down. absolutely amazing.

radiation does occur in a vacuum and heat is lost through radiation. if your "hot" object is in contact with a cold object, heat will be transfered via conduction. period. So both answers (a) and (d) are in fact correct as shown through the equations I provided above....

Answer 2

In a vacuum, heat transfer by convection doesn't happen as there is no medium for it to occur.

If the objects are in contact, then conduction will take place depending upon the Temperature Difference (High ΔT, faster heat transfer rate).
If the objects are not in contact, only heat transfer by radiation can take place...Again this depends on ΔT as above.

This brings me to say that Cooling is Proportional to Temperature (Difference).

Answer 3

If it is a vacuum there is NOTHING there; it is a VOID. So how can temperature & cooling exist. For a rate of cooling and temperature to be measured there must be matter there. Hence it is not a vacuum.

Electro-magnetic waves can pass through a vacuum, of which Infra-Red waves are part of the electro-magnetic spectrum. Infra-Red waves need to pass through matter to heat up or cool down the matter - hence it is not a vacuum.

Answer 4

Here's a hint. The reason "in a vacuum" is part of the question is that you have to consider only radiation.

The object being cooled is in a vacuum, so no conduction or convection are possible.

I hope that makes it obvious.

Answer 5

In vacuum, the heat transfer mechanism is radiation, rather than conduction or convection, You might look at black body radiation or Stefan's constant ... find out the answer yourself and you will remember it better than if you just copy it from here. ( In answer to lenpol, if energy couldn't transfer in vacuum, we wouldn't see the stars or feel the heat from the sun).

Answer 6

dT/dt = -kT