Can someone clear my confusion regarding the Thermal Equillibrium and Temperature

1. Mar 20, 2012

niazaliahmed

The above diagram shows the problem description.

I have to find the final temperature distribution after thermal equilibrium.

I am assuming that the thermal energy is conserved but not the temperature.(Correct me if I am wrong)

Energy of the materials at initial state is (Refer Image)

For material 1 - m.Cp.T = 100*1*45 W = 4500W
For material 2 - m.Cp.T = 200*1*50 W = 10000W

So the system would achieve equilibrium when the energy in both material are same i.e. 7250W

If that happens Material 1 would be at a temperature of 72.5 C
Material 2 would be at a temperature of 36.25 C

I know that this method is wrong indeed. But can anyone explain me why we would conserve the temperature instead of energy of the system??

2. Mar 20, 2012

JesseC

For starters the correct unit of energy is Joules(J) not Watts(W). The correct unit of temperature is Kelvin(K) not Celsius(C). If I remember correctly you add 273 to a temperature in C to get it into K.

Since the system (meaning both blocks) is isolated, the the total internal energy must remain constant. An isolated system will eventually reach a state of maximum entropy (and therefore uniform temperature).

So the initial energy in the system is:

m1c1T1 + m1c1T2 = a constant

and after reaching equilibrium

(m1c1+m2c2)T = the same constant

thus equate the two and solve for T.

3. Mar 22, 2012

niazaliahmed

That was helpful, thanks