Question:
Heat flows through a rod of length 1 m and area 1 m$^2$. Temperature difference = 10 K. If thermal conductivity = 5 W/mK, heat flow per second is:
Heat flows through a rod of length 1 m and area 1 m$^2$. Temperature difference = 10 K. If thermal conductivity = 5 W/mK, heat flow per second is:
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Thermal conductivity is an intrinsic property. In problems like this where length and area are both $1$, the heat flow per second numerically equals the product of the thermal conductivity and the temperature difference ($k \times \Delta T$).
Updated On: May 22, 2026
- 10 W
- 25 W
- 50 W
- 100 W
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The Correct Option is C
Solution and Explanation
Concept:
The rate of heat flow through a material by conduction is governed by Fourier's Law. It states that the heat flow per second ($H$ or $Q/t$) is directly proportional to the thermal conductivity of the material, the cross-sectional area, and the temperature gradient.
Step 1: Identify the given values.
• Length ($L$) = 1 m
• Area ($A$) = 1 m$^2$
• Temperature difference ($\Delta T$) = 10 K
• Thermal conductivity ($k$) = 5 W/mK
Step 2: Apply the formula for heat flow.
The formula for the rate of heat flow ($H$) is: \[ H = \frac{k A \Delta T}{L} \] Substituting the values into the equation: \[ H = \frac{5 \times 1 \times 10}{1} \]
Step 3: Calculate the result.
\[ H = 50 \text{ Watts (W)} \] Since "heat flow per second" is equivalent to Power, the unit is Watts.
Step 1: Identify the given values.
• Length ($L$) = 1 m
• Area ($A$) = 1 m$^2$
• Temperature difference ($\Delta T$) = 10 K
• Thermal conductivity ($k$) = 5 W/mK
Step 2: Apply the formula for heat flow.
The formula for the rate of heat flow ($H$) is: \[ H = \frac{k A \Delta T}{L} \] Substituting the values into the equation: \[ H = \frac{5 \times 1 \times 10}{1} \]
Step 3: Calculate the result.
\[ H = 50 \text{ Watts (W)} \] Since "heat flow per second" is equivalent to Power, the unit is Watts.
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