Answer
A- 12.5 W
12.5W would be the rate of heat conducted by rod B under the same circumstances as rod A.
Explanation:
Basically all you have got to do is look at the standard formula for rate of heat transfer:
R= K x A x ΔT/ d
R: rate of heat being transferred ;
K: thermal conductivity value;
A: area of contact between rod and reservoir;
ΔT: Temperature difference between hot reservoir and cold reservoir;
d: thickness of the material which heat is being conducted thru.
R= 25W for Rod A
K and ΔT stays the same for both Rods
Area for Rod A: A= π x r², therefore Area for Rod B : A= π x (2 x r)² = 4 x A, since Rod B has double the thickness affecting the radius of the Rod.
d for Rod B: 2 x d (of Rod A) as the length of the rod
Observation: Since the Rods are cylindrical shaped objects, thickness the length of the rod is seen as the thickness in the formula and the actual thickness of the rod is used to find the area of contact, everything would be different for a square shaped object.
Applying the data o collected to formula we have:
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
R for Rod B: R = 12.5W
