To find the temperature at point Q in the system of rods, we can use the concept of steady-state heat conduction along the rods. Here’s how to approach this problem:

### 1. ### Break Down the Problem
1. Identify the configuration of the rods and understand how heat will transfer through them.
2. Establish the known temperatures (A = 60°C, B = 0°C).
3. Determine how many segments exist between points A and B and consider their thermal conductivity.

### 2. ### Relevant Concepts
- For rods in a steady-state condition, we apply the principle that the temperature gradient is constant along each rod segment. This is described by the formula:

$$
\frac{T_A - T_B}{L} = \text{Constant} \quad \text{(where $L$ is the length of the segment)}
$$

### 3. ### Analysis and Detail
Assuming the rods have equal lengths and equal conductivity, we can deduce the temperatures at the intermediate points by dividing the temperature difference evenly across the segments.

1. The total temperature difference between points A and B is:
$$
\Delta T = T_A - T_B = 60°C - 0°C = 60°C
$$

2. Since there are 6 identical rods, there are 5 equal segments between point A and point B. Hence, we can find the temperature drop across each segment:
$$
\Delta T_{segment} = \frac{\Delta T}{n} = \frac{60°C}{5} = 12°C
$$

3. Now, calculate the temperatures at each point:
- Temperature at the first segment (A to 1st rod):
$$
T_1 = T_A - 12°C = 60°C - 12°C = 48°C
$$
- Temperature at the second segment (1st rod to 2nd rod):
$$
T_2 = T_1 - 12°C = 48°C - 12°C = 36°C
$$
- Temperature at the third segment (2nd rod to 3rd rod):
$$
T_3 = T_2 - 12°C = 36°C - 12°C = 24°C
$$
- Temperature at the fourth segment (3rd rod to 4th rod):
$$
T_4 = T_3 - 12°C = 24°C - 12°C = 12°C
$$
- Temperature at the fifth segment (4th rod to Q):
$$
T_Q = T_4 - 12°C = 12°C - 12°C = 0°C
$$

### 4. ### Verify and Summarize
We verified the temperatures through consistent calculations for each segment.

Consequently, the calculated temperatures at points 1 through Q are as follows:
- $T_A = 60°C$
- $T_1 = 48°C$
- $T_2 = 36°C$
- $T_3 = 24°C$
- $T_4 = 12°C$
- $T_Q = 0°C$

### Final Answer
The temperature at point Q will be $0°C$.

Question

To find the temperature at point Q in the system of rods, we can use the concept of steady-state heat conduction along the rods. Here’s how to approach this problem:

### 1. ### Break Down the Problem
1. Identify the configuration of the rods and understand how heat will transfer through them.
2. Establish the known temperatures (A = 60°C, B = 0°C).
3. Determine how many segments exist between points A and B and consider their thermal conductivity.

### 2. ### Relevant Concepts
- For rods in a steady-state condition, we apply the principle that the temperature gradient is constant along each rod segment. This is described by the formula:
  
  $$
  \frac{T_A - T_B}{L} = \text{Constant} \quad \text{(where $L$ is the length of the segment)}
  $$

### 3. ### Analysis and Detail
Assuming the rods have equal lengths and equal conductivity, we can deduce the temperatures at the intermediate points by dividing the temperature difference evenly across the segments.

1. The total temperature difference between points A and B is:
   $$
   \Delta T = T_A - T_B = 60°C - 0°C = 60°C
   $$

2. Since there are 6 identical rods, there are 5 equal segments between point A and point B. Hence, we can find the temperature drop across each segment:
   $$
   \Delta T_{segment} = \frac{\Delta T}{n} = \frac{60°C}{5} = 12°C
   $$

3. Now, calculate the temperatures at each point:
   - Temperature at the first segment (A to 1st rod):
     $$
     T_1 = T_A - 12°C = 60°C - 12°C = 48°C
     $$
   - Temperature at the second segment (1st rod to 2nd rod):
     $$
     T_2 = T_1 - 12°C = 48°C - 12°C = 36°C
     $$
   - Temperature at the third segment (2nd rod to 3rd rod):
     $$
     T_3 = T_2 - 12°C = 36°C - 12°C = 24°C
     $$
   - Temperature at the fourth segment (3rd rod to 4th rod):
     $$
     T_4 = T_3 - 12°C = 24°C - 12°C = 12°C
     $$
   - Temperature at the fifth segment (4th rod to Q):
     $$
     T_Q = T_4 - 12°C = 12°C - 12°C = 0°C
     $$

### 4. ### Verify and Summarize
We verified the temperatures through consistent calculations for each segment.

Consequently, the calculated temperatures at points 1 through Q are as follows:
- $T_A = 60°C$
- $T_1 = 48°C$
- $T_2 = 36°C$
- $T_3 = 24°C$
- $T_4 = 12°C$
- $T_Q = 0°C$

### Final Answer
The temperature at point Q will be $0°C$.

Knowee AI · Accepted Answer