# time it takes to reach equilibrium

by Pengwuino
Tags: equilibrium, reach, takes, time
 PF Patron P: 7,122 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?
 P: 618 Peng, Hint: What if one reservoir were at 200 degrees. How long would it take for the ball to get to 200 degrees?
 PF Patron P: 7,122 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.
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HW Helper
P: 2,795

## time it takes to reach equilibrium

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.
 PF Patron Sci Advisor Thanks Emeritus P: 38,428 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.
 PF Patron P: 7,122 Whats the formula for this?
 Sci Advisor P: 5,096 $$q = h*a \Delta T$$ 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
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