The temperature gradient across a copper rod of thickness 0.02m, maintained at two temperature junctions of 20º and 80ºC respectively is?

1. Analyze the Question

We are asked to calculate the temperature gradient across a copper rod. We are given:

• Thickness of the rod ($L$) = $0.02 \, \text{m}$
• Temperature at the first junction ($T_1$) = $20^\circ\text{C}$
• Temperature at the second junction ($T_2$) = $80^\circ\text{C}$

2. Explain the Concept

The temperature gradient is defined as the rate of change of temperature with respect to distance. It represents how much the temperature changes per unit length of the material.

The formula is:

Where:

• $\Delta T$ is the temperature difference ($T_2 - T_1$)
• $L$ is the thickness (or length) of the material

3. Show the Solution

Step 1: Calculate the temperature difference ($\Delta T$)

Step 2: Apply the formula

Step 3: Simplify the calculation To make the division easier, multiply both the numerator and the denominator by 100:

Step 4: Convert to standard form

(Note: In physics, a change in temperature of $1^\circ\text{C}$ is equivalent to a change of $1 \, \text{K}$, so the unit $\text{K/m}$ is correct.)

4. Identify the Answer

Comparing our result ($3.0 \times 10^3 \, \text{K/m}$) with the given options, it matches Option B.

5. Exam Tip

When calculating gradients (whether temperature, velocity, or pressure), always ensure your units are consistent. If the thickness were given in centimeters, you would have to convert it to meters first to match the standard SI unit of $\text{K/m}$. Don't let the decimal points confuse you—moving the decimal two places to the right for the denominator ($0.02 \rightarrow 2$) means you must also move the decimal two places for the numerator ($60 \rightarrow 6000$).