Topic: Help in Calculus?

[jrlibrarian]

Hey guys,


Just got into differential equations, and I need some help if possible.


Assume that heat is supplied at a constant rate, R. The rate at which heat is stored is directly proportional to the rate of change in temperature. Let T be the number of degrees above room temperature. Let t be the elapsed time, in seconds, since heat was applied. Then the storage rate is C(dT/dt). The proportionality constant, C, (calories per degree) is the heat capacity of the heater materials. According to Newton's Law of Cooling, the rate at which heat is lost to the room is directly proportional to T. The (positive) proportionality constant, h, is called the heat transfer coefficient.


a. The rate at which heat is supplied to the heater is equal to the sum of the storage rate and the loss rate. Write a differential equation that expresses this fact.
How exactly do I do this? And help possible will be great.
Thanks

[apdude]

So your adding energy to the heater and it's conducted through the heater to the edge of the heater where it is convected away by the room.  So basically you want to find out when the temperature doesn't change so it is when the derivitive equals 0.  It has been a while since I had to use thermodynamics though.

[stevey]

I don't think it asked to solve anything, it just want dH written as a function of T and dT/dt. The storage rate is given as C(dT/dt) and Newton's Law of Cooling is -h*T.
^dH/_dt=C*^dT/_dt-h*T

[jrlibrarian]

I don't think it asked to solve anything, it just want dH written as a function of T and dT/dt. The storage rate is given as C(dT/dt) and Newton's Law of Cooling is -h*T.
^dH/_dt=C*^dT/_dt-h*T

Thanks! Just had no idea how the hell to get started.

[Halbred]

THE BIG YELLOW ONE'S THE SUN.

[ThePerm]

x + y = x + y

[BlackNMild2k1]