Question

two identical blocks are heated to different temperatures. the blocks are placed so that they touch, and heat begins to flow between the blocks. the pair of blocks is insulated, so no energy escapes. later, the temperature of each block is measured again. which pair of temperatures is possible?

Explanation:

Step1: Understand heat - transfer principle

Heat flows from a higher - temperature object to a lower - temperature object until thermal equilibrium is reached. In an insulated system (no energy loss to the surroundings), the total internal energy is conserved. The initial temperatures are $T_1 = 142^{\circ}C$ and $T_2=206^{\circ}C$. The final temperatures of the two blocks must be the same when thermal equilibrium is achieved.

Step2: Analyze each option

• Option 1: Temperatures $0^{\circ}C$ and $64^{\circ}C$ are both lower than the initial temperatures, which is not possible as there is no heat loss to the outside and heat transfer occurs between the two blocks only.
• Option 2: Temperatures $129^{\circ}C$ and $219^{\circ}C$ have one temperature lower and one higher than the initial temperatures in a non - consistent way with heat transfer. Heat cannot make one block cooler and the other warmer in an insulated system with no external influence.
• Option 3: Temperatures $174^{\circ}C$ and $174^{\circ}C$ indicate that thermal equilibrium has been reached. The average of the initial temperatures $\frac{142 + 206}{2}=\frac{348}{2}=174^{\circ}C$. When thermal equilibrium is achieved in an insulated system with two identical objects, they will have the same final temperature which is the average of their initial temperatures (since they have the same heat - capacity as they are identical).

Answer:

The pair of temperatures $174^{\circ}C$ for Block 1 and $174^{\circ}C$ for Block 2 is possible.