Chapter5, Lesson C - Thermal Equilibration of a Copper Block with an Iron Block

5C-10 :	Thermal Equilibration of a Copper Block with an Iron Block								5 pts

A 50 kg block of copper at 0°C and a 100 kg block of iron at 200°C are brought into contact in an insulated space. Predict the final equilibrium temperature.

Read :	The mass and initial temperature of each block are given. We know that the equilibrium temperature of the blocks must lie between the two intial temperatures. We will need to look-up the heat capacity or specific heat of both copper and iron. Then, we can apply the 1st Law to a system made up of the two blocks. No work or heat transfer crosses the boundary of this system during the approach to equilibrium, so the only unknown in the equation is the final, equilibrium temperature. So, we can solve for it and evaluate it.






Given:	mCu	50	kg			mFe	100	kg
	TCu,1	0	°C			TFe,1	200	°C

Find:	T2	???	°C

Assumptions:		Copper and iron have constant heat capacities. No heat is exchanged with the surroundings by either the copper or the iron. Copper and iron are both incompressible, so this process is a constant volume process.

Equations:	We begin by writing the 1st Law and we choose as our system the oil and the copper.

									Eqn 1

	By cleverly selecting our system, Q = 0 and W = 0. This makes the solution simpler.

	Because both oil and copper are assumed to be incompressible with constant heat capacities:
									Eqn 2

Solve:	Substitute Eqn 2 into Eqn 1 twice, once for copper and once for iron to get :

									Eqn 3

	Notice that there is only one T2 because in the final, equilibrium state, the copper and the iron are both at the same temperature !


	Now, solve Eqn 3 for T2:

									Eqn 4

									Eqn 5

	Before we can evaluate T2, we must look up the specific heat of iron and of copper.

	Online, I found just one value for iron:					CP,Fe	0.448	kJ/kg-K
	For incompressible solids, CV = CP, so :					CV,Fe	0.448	kJ/kg-K

	For copper, I found three values of CP :					T (°C)	-100	0	100
						CV = CP (kJ/kg-K)	0.328	0.381	0.393

	Since T2 will lie between 0°C and 200°C, it would be best to use the average of the CV values at 0°C and 100°C.

					Average	CV,Cu	0.387	kJ/kg-K

	Now, we can finally plug numbers into Eqn 5 and evaluate T2:
						T2	139.7	°C

Verify Assumption:		None of the assumptions can be verified.

Answer Questions:		T2	139.7	°C

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