Question

The rate of flow of heat through a copper rod with a temperature difference of $28^\circ\text{C}$ is $1400\text{ cal}\cdot\text{s}^{-1}$. The thermal resistance of the copper rod will be

• A. $0.05^\circ\text{C}\cdot\text{s}\cdot\text{cal}^{-1}$
• B. $0.02^\circ\text{C}\cdot\text{s}\cdot\text{cal}^{-1}$
• C. $5^\circ\text{C}\cdot\text{s}\cdot\text{cal}^{-1}$
• D. $2^\circ\text{C}\cdot\text{s}\cdot\text{cal}^{-1}$

Hint:

Always double-check the unit layout in the options to make sure your calculation is set up correctly. The unit $^\circ\text{C}\cdot\text{s}\cdot\text{cal}^{-1}$ clearly dictates that temperature ($^\circ\text{C}$) belongs in the numerator and heat rate ($\text{cal}/\text{s}$) belongs in the denominator!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Given heat conduction rate Q=1400 cal/s through a copper rod with ΔT=28°C, find its thermal resistance R_H.

Step 2: Key Formula or Approach:
Thermal resistance is defined analogously to electrical resistance: R_H = ΔT / Q.

Step 3: Detailed Explanation:
R_H = 28°C / 1400 cal·s⁻¹ = 28/(14×100) = 2/100 = 0.02 °C·s·cal⁻¹.

Step 4: Final Answer:
Thermal resistance is 0.02 °C·s·cal⁻¹, matching option (B).