The temperature gradient in a rod of `0.5 m` length is `80^(@)C//m`. It the temperature of hotter end of the rod is `30^(@)C`, then the temperature of the cooler end is

Options

A. `0^(@)`C
B. `-10^(@)`C
C. `10^(@)`C
D. `40^(@)`C

Explanation

To find the temperature at the cooler end of the rod, we can use the formula for temperature gradient. The temperature gradient (G) is defined as the change in temperature (Δθ) per unit length (L) of the rod.

### Step-by-Step Solution:

1. **Identify the given values:**
- Length of the rod (L) = 0.5 m
- Temperature gradient (G) = 80 °C/m
- Temperature at the hotter end (θ1) = 30 °C

2. **Use the formula for temperature gradient:**
\[ G = \frac{\theta_1 - \theta_2}{L} \]
where:
- θ1 = temperature at the hotter end
- θ2 = temperature at the cooler end

3. **Rearrange the formula to find θ2:**
\[ \theta_2 = \theta_1 - G \cdot L \]

4. **Substitute the known values into the equation:**
\[ \theta_2 = 30 °C - (80 °C/m \cdot 0.5 m) \]

5. **Calculate the value:**
\[ \theta_2 = 30 °C - 40 °C = -10 °C \]

6. **Conclusion:**
The temperature at the cooler end of the rod is -10 °C.