Question

70°c block 1, 46°c block 2. later, the temperature of each block is measured again. which pair of temperatures is possible? options: 67°c (block 1) & 43°c (block 2); 54°c (block 1) & 62°c (block 2); 62°c (block 1) & 54°c (block 2); 70°c (block 1) & 58°c (block 2).

Explanation:

Step1: Recall heat transfer principle

Heat flows from higher temp to lower temp. Initial temps: Block1 = \(70^\circ\text{C}\), Block2 = \(46^\circ\text{C}\). So Block1 should cool (temp decrease), Block2 should warm (temp increase), until thermal equilibrium (or closer).

Step2: Analyze each option

- Option 1: Block1 (\(67^\circ\text{C}\), decrease) & Block2 (\(43^\circ\text{C}\), decrease) → Block2 cools (wrong, should warm). Reject.
- Option 2: Block1 (\(54^\circ\text{C}\), decrease) & Block2 (\(62^\circ\text{C}\), increase) → Block2 temp > Block1? Initial Block1 > Block2. Heat flows from 1→2, so Block2 can’t exceed Block1’s initial temp? Wait, no—eventually, they approach equilibrium. Wait, initial Block1:70, Block2:46. Equilibrium temp is between 46 and 70. Let's check:
- Option 2: 54 (between 46-70) and 62 (between 46-70). Block1 decreased (70→54), Block2 increased (46→62). Possible (heat transfer: 1 loses heat, 2 gains, until equilibrium or closer).
- Option 3: Block1 (\(62^\circ\text{C}\), decrease) & Block2 (\(54^\circ\text{C}\), increase? 46→54 is increase, but Block1 (62) > Block2 (54). But let's check temp change: Block1:70→62 (decrease), Block2:46→54 (increase). But wait, equilibrium should be between 46 and 70. But let's see the other option.
- Option 4: Block1 (\(70^\circ\text{C}\), no change) & Block2 (\(58^\circ\text{C}\), increase). But Block1 temp same, so no heat transfer (since heat transfer needs temp difference). So Block2 can’t warm if Block1 temp doesn’t change. Reject.

Wait, recheck Option 2: Block1 54 (decrease from 70), Block2 62 (increase from 46). The key is heat flows from high to low. So Block1 (hotter) loses heat (temp down), Block2 (colder) gains heat (temp up). The equilibrium temp is between 46 and 70. Let's check the temp changes:

- Option 2: 54 (Block1) and 62 (Block2). The average of initial temps: \(\frac{70 + 46}{2} = 58^\circ\text{C}\). So 54 and 62 are around 58, with Block1 below, Block2 above? Wait, no—heat flows until they are equal or closer. Wait, maybe I made a mistake. Let's re-express:

Initial: Block1 (70) > Block2 (46). So after heat transfer, Block1’s temp (\(T_1\)) < 70, Block2’s temp (\(T_2\)) > 46, and \(T_1 \geq T_2\) (since heat stops when equal; if not equal, \(T_1 > T_2\) but closer). Wait, no—if Block2’s temp exceeds Block1’s, that would mean heat flowed from 2→1, which is impossible (since initial 1 is hotter). So \(T_2\) must be ≤ \(T_1\) (after transfer), and \(T_1 < 70\), \(T_2 > 46\).

Now check options:

1. \(T_1=67\), \(T_2=43\): \(T_2=43 < 46\) (decrease, wrong). Reject.
2. \(T_1=54\), \(T_2=62\): \(T_2=62 > T_1=54\) → heat would flow from 2→1, but initial 1 was hotter. Impossible. Wait, I messed up earlier.
3. \(T_1=62\), \(T_2=54\): \(T_1=62 < 70\) (decrease), \(T_2=54 > 46\) (increase), and \(T_1 > T_2\) (62 > 54). Possible (heat flows from 1→2, 1 cools to 62, 2 warms to 54, still 1 hotter than 2, moving toward equilibrium).
4. \(T_1=70\), \(T_2=58\): \(T_1\) same (no heat transfer), so \(T_2\) can’t warm (needs temp difference). Reject.

Wait, now I see my mistake. In Option 2, \(T_2=62 > T_1=54\) implies heat flows from 2 to 1, but initial 1 was hotter. So that’s impossible. So Option 3: \(T_1=62\) (decrease from 70), \(T_2=54\) (increase from 46), and \(T_1 > T_2\) (62 > 54) → possible, as heat flows from 1 to 2, 1 cools, 2 warms, and 1 is still hotter (moving toward equilibrium, which would be between 54 and 62, or closer to 58).

Wait, let's recalculate equilibrium. The heat lost by Block1 = heat gained by Block2 (assuming same mass and specific heat, but even without, the temp change should be such that \(T_1\) decreases, \(T_2\) increases, and \(T_1 \geq T_2\)).

Initial: 70 (B1), 46 (B2).

Option 3: B1=62 (ΔT= -8), B2=54 (ΔT= +8). So equal magnitude of temp change (if same mass/c), which is possible.

Option 2: B1=54 (ΔT= -16), B2=62 (ΔT= +16). But then B2 is hotter than B1, which would require heat to flow back, impossible.

So correct option is the third one? Wait, the options are:

First row: left (67,43), right (54,62)

Second row: left (62,54), right (70,58)

So the second row left: 62°C (Block1), 54°C (Block2).

Yes, that’s possible. Because Block1 (70→62, decrease) and Block2 (46→54, increase), and 62 > 54 (so heat still flows from 1 to 2, moving toward equilibrium).

Answer:

The possible pair is \(62^\circ\text{C}\) (Block 1) and \(54^\circ\text{C}\) (Block 2) (the third option, second row left).