# Temperature graph slope

1. Jul 24, 2013

### ShizukaSm

In a series of experiments, block B is to be placed in a thermally insulated container with
block A, which has the same mass as blockB. In each experiment, block B is initially at a certain temperature TB, but temperature TA of block A is changed from experiment to experiment. Let Tf
represent the final temperature of the two blocks when they reach thermal equilibrium in any of the experiments. The graph(attatched) gives temperature Tf versus the initial temperature TA for a range of possible values of TA, from TA = 0 K to TA = 500 K. The vertical axis scale is set by Tfs= 400 K. What are:
(a)temperature TB.
(b) the ratio cB/cA of the specific heats of the blocks?

Ok so, I was able to solve this problem, however, my book answer used a method that I did not understand:

How can he infer that the slope is equal to $\frac{c_A}{c_A+c_B}$? Where did that come from?

2. Jul 24, 2013

### Mandelbroth

Rewriting the expression as $T_f=\left(\frac{c_A}{c_A+c_B}\right) T_A+\left(\frac{c_B}{c_A+c_B}\right) T_B$ might help.

3. Jul 24, 2013

### ShizukaSm

Oh, yes it does! Thanks a lot

4. Jul 24, 2013

### Mandelbroth

You're most certainly welcome. Good luck with the physics.