Final answer:
The rate of heat flow by conduction through a slab becomes Hcond / 4 when the slab's thickness is doubled, its cross-sectional area is halved, and the temperature difference across it is doubled. Therefore, the correct answer is D) Hcond / 4.
Step-by-step explanation:
When evaluating how the rate of heat flow by conduction through a slab changes with various modifications to the slab's properties, we see that the original flow rate is Hcond. If the slab thickness is doubled, the cross-sectional area is halved, and the temperature difference across it is doubled, we must apply the formula of conductive heat transfer: Q/t = kA(T2 - T1)/d. In this formula, k is the thermal conductivity, A is the cross-sectional area, and d is the thickness of the material.
The original rate of heat flow is Hcond. When the thickness doubles, the denominator of our formula doubles, reducing the heat transfer rate by half. However, halving the cross-sectional area also reduces the rate by half again. Yet, doubling the temperature difference doubles the rate of heat transfer. Combining these changes, the rate of heat flow becomes Hcond / 2 * 1/2 * 2, which simplifies to Hcond / 4. Therefore, the correct answer is D) Hcond / 4.