Finding Final Temp. Distribution After Thermal Equilibrium

[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??

 

[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.

 

[niazaliahmed]

That was helpful, thanks