Answer
A- 12.5 W
Rod B would conduct heat at a rate of 12.5 W under the same conditions as rod A.
Explanation:
You need to refer to the basic equation for heat transfer:
R= K x A x ΔT/ d
R: denotes the rate of heat transfer;
K: the thermal conductivity;
A: the contact area between the rod and the reservoir;
ΔT: the temperature difference between the hot and cold reservoirs;
d: the thickness of the material through which heat travels.
R= 25W for Rod A.
K and ΔT remain constant for both rods.
For Rod A: A= π x r²; thus for Rod B, A= π x (2 x r)² = 4 x A, since Rod B's thickness is doubled affecting the radius.
d for Rod B is 2 x d (of Rod A) due to the length of the rod.
Observation: Given that the rods are cylindrical, the length is treated as thickness in the formula, while the actual thickness is used for area calculations, leading to different considerations for square-shaped objects.
Using the derived details in the equation gives us:
25= K x 4 x A x ΔT / 2d
25/2 = K x A x ΔT / d
12.5= K x A x ΔT / d
The rate for Rod B: R = 12.5W