Time it takes to reach equilibrium

1. Apr 2, 2005

Pengwuino

Ok lets say i have a metal ball at 50 C and 2 thermal reservoirs at 300 C and 500 C.

Will the metal ball reach 200C faster in the 300C or 500C reservoir? (Sorry the title name is misleading). Basically, the question is there a relation between temperature and the time it takes to transfer energy or is the tim relationship only dependant on the type of material being used?

2. Apr 2, 2005

jdavel

Peng,

Hint: What if one reservoir were at 200 degrees. How long would it take for the ball to get to 200 degrees?

3. Apr 3, 2005

Pengwuino

Thats what i want to know and i want to know the relationship to the temperature. Will the ball reach 200 faster in a 300C reservoir or a 500C reservoir? Or is the time it takes only dependant on the materials used.

4. Apr 3, 2005

Q_Goest

Heat transfer is always a function of the difference in temperature, so given a ball at 50 C, if the only difference is environment temperature, it will warm faster in the hotter environment.

5. Apr 3, 2005

HallsofIvy

Staff Emeritus
Newton's law of cooling (or heating): Heat moves from the hotter environment to the cooler at a rate proportional to the difference in temperatures. In this case, the heat moves from the reservoir to the metal ball at a rate proportional to the difference in temperatures: heat moves faster from the higher temperature environment and so the ball heats faster.

6. Apr 3, 2005

Pengwuino

Whats the formula for this?

7. Apr 4, 2005

FredGarvin

$$q = h*a \Delta T$$ where:

q = rate of heat transfer (watts usually)
h = heat transfer coefficient (in w/m^2*K)
a = effective area (m^2)
Delta T = temperature difference (K)

You may also see it in the form of:
$$q'' = h \Delta T$$ where:

q'' = heat density in W/m^2

Last edited: Apr 4, 2005
8. Apr 5, 2005

Gokul43201

Staff Emeritus
You missed the point of jdavel's hint. If the reservoir itself is at exactly 200C, it will take an infinitely long time to reach 200C. So, is that not indicative of what your answer should be ?

The shape of the heating/cooling curve is an exponential growth/decay. The driving force is the temperature gradient.