How Does Thermal Equilibrium Determine Final Temperature Between Copper Blocks?

[redline7890]

Two identical copper blocks of mass m grams, one at (fundamental) temperature T1
and the other at temperature T2 are brought into thermal contact until they reach
thermodynamic equilibrium. The heat capacity of copper/gram is Cv .
What is the final temperature Tf?

 

[Andrew Mason]

Two identical copper blocks of mass m grams, one at (fundamental) temperature T1
and the other at temperature T2 are brought into thermal contact until they reach
thermodynamic equilibrium. The heat capacity of copper/gram is Cv .
What is the final temperature Tf?

Heat would, of course, flow from the hotter block to the colder block until they both reach the same temperature. Whatever heat flows out of the hot block flows into the cold block.

$$\Delta Q_1 = cm\Delta T_1$$
$$\Delta Q_2 = cm\Delta T_2$$
$$\Delta Q_1 + \Delta Q_2 = 0$$

And, of course:

$$T_1 + \Delta T_1 = T_f$$
$$T_2 + \Delta T_2 = T_f$$

(Note: One of the temperature changes is negative and one is positive).

You can work out what Tf is from the above.

Or you can observe that since the blocks are identical - same mass and same heat capacity - the relationship between the drop in temperature of the hotter block and the increase in temperature for the colder block is ____________?

AM