Heat Capacity and Thermal Equilibrium

[MaryCate22]

Homework Statement

A 3.50-kg block of iron initially at 8.00 × 10^2 K is placed on top of a 6.25-kg block of copper initially at 4.00 × 10^2 K. Assume the blocks are thermally insulated from their surroundings but not from each other and that they constitute a closed system.

How much energy is transferred thermally from the iron to the copper as the two blocks come to thermal equilibrium?

Homework Equations

heat capacity=amount of energy transferred thermally (J)/resulting change in temperature
specific heat capacity (c) =amount of energy required to raise 1 kg of a certain material by 1 degree Kelvin (J/K*kg)

c of copper is 385, c of iron is 449

The Attempt at a Solution

Thermal equilibrium would be (400+800)/2=600. So during this process the copper would be raised 200 K. Using the specific heat capacity of copper 385 J/K*kg, I found that it would be 2406.25 J to raise 6.25 kgs of it by 1 K. To Raise 200 K it would be (2406.25)(200)=481250 J.

This is incorrect, however. What am I missing?

 

[haruspex]

Thermal equilibrium would be (400+800)/2=600.

No. Any other thoughts?

 

[MaryCate22]

No. Any other thoughts?

They do not contribute to the equilibrium temperature equally do they? I looked up a formula for finding equilibrium temp and otherwise worked it out the same. I got the right answer, thanks!

Formula for Equilibrium Temperature: c1m1(Tf-Ti)=c2m2(Tf-Ti)

-(449)(3.5)(Tf-800)=(385)(6.25)(Tf-400) Final Temperature= 558 K, so the copper is only raised 158 degrees.

 

[haruspex]

I got the right answer

Good job.