To determine which pair of temperatures is possible, let’s analyze the conditions given:

1. Initial Temperatures:

   • Block 1: 24°C
   • Block 2: 144°C

2. Energy Exchange:

   • Since no energy escapes, the system is isolated, and the total energy remains constant. This implies that the average temperature should stay consistent as thermal equilibrium is approached.
   • The average temperature of both blocks initially is: $\text{Average Temperature} = \frac{24^\circ \text{C} + 144^\circ \text{C}}{2} = 84^\circ \text{C}$

3. Evaluating Each Option:

   • We need a pair of temperatures whose average is also 84°C, as no energy is added or lost.

   Let's check each option:

   • Option 1: Block 1: 105°C, Block 2: 63°C $\text{Average} = \frac{105^\circ \text{C} + 63^\circ \text{C}}{2} = 84^\circ \text{C} \quad (\text{Correct})$
   • Option 2: Block 1: 131°C, Block 2: 144°C $\text{Average} = \frac{131^\circ \text{C} + 144^\circ \text{C}}{2} = 137.5^\circ \text{C} \quad (\text{Incorrect})$
   • Option 3: Block 1: 72°C, Block 2: 192°C $\text{Average} = \frac{72^\circ \text{C} + 192^\circ \text{C}}{2} = 132^\circ \text{C} \quad (\text{Incorrect})$
   • Option 4: Block 1: 78°C, Block 2: 90°C $\text{Average} = \frac{78^\circ \text{C} + 90^\circ \text{C}}{2} = 84^\circ \text{C} \quad (\text{Correct})$

4. Conclusion:

   • The possible pairs of temperatures are:
     • Option 1: 105°C and 63°C
     • Option 4: 78°C and 90°C

Would you like a more detailed explanation or have any questions?

Here are some related questions that expand on this concept:

1. Why does the total energy remain constant in an isolated system?
2. How does thermal equilibrium affect temperature distribution between two objects?
3. What factors determine the rate of heat transfer between objects?
4. Can thermal equilibrium be reached if one of the blocks has a much higher specific heat?
5. How would the analysis change if the system were not isolated?

Tip: Always check the average temperature in a closed system problem to ensure energy conservation.