How Does Thermal Equilibrium Determine Final Temperature Between Copper Blocks?

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SUMMARY

When two identical copper blocks, each with mass m grams and specific heat capacity Cv, are brought into thermal contact, they reach thermodynamic equilibrium at a final temperature Tf. The heat transfer between the blocks is governed by the equations ΔQ1 = cmΔT1 and ΔQ2 = cmΔT2, where ΔQ1 and ΔQ2 represent the heat lost and gained, respectively. The final temperature Tf can be calculated using the relationship T1 + ΔT1 = Tf and T2 + ΔT2 = Tf, confirming that the temperature change of the hotter block is equal in magnitude but opposite in sign to that of the colder block.

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redline7890
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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?
 
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redline7890 said:
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
 

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