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: Recall heat - transfer principle

Heat flows from a hotter object to a colder object until thermal equilibrium is reached. The initial temperatures are $T_1 = 67^{\circ}C$ and $T_2=5^{\circ}C$. The final temperatures of the two - block system (insulated, so no heat loss to the surroundings) should satisfy the condition that the temperature of the initially hot block decreases and the temperature of the initially cold block increases.

Step2: Analyze each option

• Option 1: Block 1 goes from $67^{\circ}C$ to $15^{\circ}C$ (decrease) and Block 2 goes from $5^{\circ}C$ to $57^{\circ}C$ (increase). This is consistent with heat - transfer.
• Option 2: Block 1 remains at $67^{\circ}C$, which is not possible as heat must flow from it to the colder block, so this option is incorrect.
• Option 3: Block 1 increases from $67^{\circ}C$ to $122^{\circ}C$ which is not possible since it is the heat - donor in this system, so this option is incorrect.
• Option 4: Block 1 goes from $67^{\circ}C$ to $57^{\circ}C$ (decrease) and Block 2 goes from $5^{\circ}C$ to $15^{\circ}C$ (increase). This is consistent with heat - transfer.

Answer:

The possible pairs are the ones where the temperature of the initially hot block (Block 1 with initial temperature $67^{\circ}C$) decreases and the temperature of the initially cold block (Block 2 with initial temperature $5^{\circ}C$) increases. So the possible pairs are: Block 1: $15^{\circ}C$, Block 2: $57^{\circ}C$ and Block 1: $57^{\circ}C$, Block 2: $15^{\circ}C$