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Time it takes to reach equilibrium 
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#1
Apr205, 08:25 PM

PF Gold
P: 7,120

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
Apr205, 09:21 PM

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? 


#3
Apr305, 04:08 AM

PF Gold
P: 7,120

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
Apr305, 06:31 AM

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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.



#5
Apr305, 11:56 AM

Math
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Thanks
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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.



#7
Apr405, 06:59 AM

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P: 5,095

[tex]q = h*a \Delta T[/tex] 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: [tex]q'' = h \Delta T[/tex] where: q'' = heat density in W/m^2 


#8
Apr505, 04:17 PM

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


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