Math Problem Statement

Later, the temperature of each block is measured again. Which pair of temperatures is possible?

Solution

To solve this problem, we need to assess which pair of temperatures is possible given the initial temperatures and likely rules for heat transfer between the blocks. The initial temperatures are:

  • Block 1: 197°C
  • Block 2: 224°C

Since heat typically flows from a hotter object to a cooler one, we can expect that Block 2 (initially hotter) would transfer some heat to Block 1 (initially cooler). Over time, their temperatures would move closer to each other but may not necessarily equalize.

Let's examine each answer choice:

  1. 201°C (Block 1) and 220°C (Block 2):

    • These temperatures are close to the initial ones and have moved slightly towards each other. This could be a plausible pair.
  2. 222°C (Block 1) and 199°C (Block 2):

    • This suggests that Block 1 became significantly warmer than Block 2, which is unlikely because Block 1 started cooler. Heat would not naturally flow to make Block 1 hotter than Block 2 unless an external source was applied.
  3. 212°C (Block 1) and 239°C (Block 2):

    • Both blocks have become hotter, which would require an additional heat source, as heat transfer alone would not raise the temperature of both blocks. Thus, this is unlikely.
  4. 197°C (Block 1) and 216°C (Block 2):

    • Block 2 has decreased, but Block 1 has stayed the same. This is unusual as it implies Block 1 did not gain any heat while Block 2 lost heat, which is improbable in a closed system.

Based on these observations, the most likely answer is the first option: 201°C for Block 1 and 220°C for Block 2.

Would you like more details on the reasoning, or have any questions? Here are some related questions to consider:

  1. How does heat transfer typically occur between two objects of different temperatures?
  2. Why might it be impossible for both blocks to increase in temperature without an external heat source?
  3. What conditions could cause one block to stay at the same temperature while the other cools down?
  4. How would the temperatures change if Block 1 and Block 2 had different materials or thermal conductivities?
  5. What real-life scenarios could involve a similar heat transfer process between two objects?

Tip: In closed systems, heat flows from warmer to cooler areas until thermal equilibrium is reached, barring any external energy input.

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Math Problem Analysis

Mathematical Concepts

Heat Transfer
Thermal Equilibrium

Formulas

Heat flows from a higher temperature to a lower temperature until equilibrium is reached

Theorems

Law of Heat Transfer

Suitable Grade Level

Grades 5-7