Question

Two bars are conducting heat from a region of higher temperature to one of lower temperature. The bars have identical lengths and cross-sectional areas, but are made from different materials. In the drawing they are placed in "parallel" between the two temperature regions arrangement A, while they are placed end-to-end in arrangement B. In which arrangement is the heat conducted the greatest?

A) Arrangement A
B) The heat conducted is the same in both arrangements.
C) Arrangement B
D) It is not possible to determine which arrangement conducts more heat

Answer 1

A) Arrangement A

Step-by-step explanation:

The rate of heat conduction is given by Fourier's Law of Heat Conduction. It is given as follows:

Q = KAΔT/L

where,

Q = Rate of Heat Transfer or Conduction

K = Thermal Conductivity

A = Cross-Sectional Area

ΔT = Difference in Temperature

L = Thickness

So, it is clear from the formula that for a constant temperature difference and value of thermal conductivity, the rate of heat transfer is directly proportional to the cross-sectional area and it is inversely proportional to the thickness.

Therefore, the arrangement with larger cross-sectional area and smaller thickness will be the one with the greatest heat transfer rate and as a result greatest heat shall be conducted through that arrangement.

It is clear that the parallel arrangement that is arrangement A, has higher cross-sectional area and smaller thickness. Therefore, the correct option is:

A) Arrangement A