To determine the temperature gradient across a copper rod, we need to understand the concept of temperature gradient and how it is calculated. The temperature gradient is defined as the change in temperature per unit distance. It can be mathematically expressed as: \[ \text{Temperature Gradient} (G) = \frac{\Delta T}{\Delta x} \] where: - \(\Delta T\) is the change in temperature (in degrees Celsius or Kelvin), - \(\Delta x\) is the thickness of the rod (in meters). ### Step-by-Step Calculation 1. **Identify the temperatures at the two junctions**: - The temperature at one end of the rod is \(T_1 = 20°C\). - The temperature at the other end of the rod is \(T_2 = 80°C\). 2. **Calculate the change in temperature (\(\Delta T\))**: \[ \Delta T = T_2 - T_1 = 80°C - 20°C = 60°C \] 3. **Identify the thickness of the rod (\(\Delta x\))**: - The thickness of the rod is given as \(0.02 m\). 4. **Calculate the temperature gradient (G)**: \[ G = \frac{\Delta T}{\Delta x} = \frac{60°C}{0.02 m} \] 5. **Perform the division**: \[ G = \frac{60}{0.02} = 3000 \, \text{°C/m} \] 6. **Convert °C/m to K/m**: - Since the change in temperature in Celsius is equivalent to the change in Kelvin, we can express the gradient as: \[ G = 3000 \, \text{K/m} \] 7. **Express in scientific notation**: \[ G = 3.0 \times 10^3 \, \text{K/m} \] ### Conclusion The correct option is **B. 3.0 x 10^3 K/m**. ### Explanation of Other Options - **Option A: 3.0 x 10^2 K/m**: This value is too low. It suggests a much smaller temperature change per unit distance than what we calculated. - **Option C: 5.0 x 10^3 K/m**: This value is too high. It implies a steeper gradient than what is physically possible given the temperature difference and the thickness of the rod. - **Option D: 3.0 x 10^4 K/m**: This is an even larger value, which is unrealistic for the given temperatures and thickness. It suggests an extreme temperature change per unit distance that does not match our calculations. ### Common Pitfalls - **Confusing temperature units**: Remember that a change in temperature in Celsius is equivalent to a change in Kelvin for the purpose of calculating gradients. - **Miscalculating the thickness**: Ensure that the thickness is in meters when performing calculations. - **Forgetting to convert units**: Always check if the final answer needs to be in a specific unit or format. ### Revision Summary - The temperature gradient is calculated using the formula \(G = \frac{\Delta T}{\Delta x}\). - For a temperature change of 60°C across a thickness of 0.02 m, the gradient is \(3.0 \times 10^3 \, \text{K/m}\). - Ensure to use consistent units and double-check calculations to avoid errors. - Understand the physical meaning of the temperature gradient in the context of heat transfer.