If the temperature gradient doubles in Fourier's law, how does Qdot change?

If the temperature gradient doubles in Fourier's law, how does Qdot change?

• A. Increases by a factor of 4
• B. Remains unchanged
• C. Increases by a factor of 2
• D. Decreases by half

Answer: (C)

Fourier's law shows heat transfer rate is directly proportional to the temperature gradient. In one-dimensional steady conduction with constant k and cross-sectional area, Qdot = -k A (dT/dx). The minus sign indicates direction from hot to cold, so focus on the magnitude: Qdot ∝ dT/dx. If the temperature gradient doubles, the driving force for heat flow doubles, so the amount of heat transferred per unit time also doubles. Therefore the correct outcome is that Qdot increases by a factor of two.

Fourier's law shows heat transfer rate is directly proportional to the temperature gradient. In one-dimensional steady conduction with constant k and cross-sectional area, Qdot = -k A (dT/dx). The minus sign indicates direction from hot to cold, so focus on the magnitude: Qdot ∝ dT/dx. If the temperature gradient doubles, the driving force for heat flow doubles, so the amount of heat transferred per unit time also doubles. Therefore the correct outcome is that Qdot increases by a factor of two.