Rod a and rod b are cylindrical rods made of the same metal. amd they differ only in size. rod b has double the length and double the width of rod a. in an experiment, rod a is found to comduct heat at a rate of 25 w between a hot reservoir and a cold reservoir. at what width of rod a. rate will rod b conduct heat between the same two reservoirs?
a.12.5 w
b.100 w
c. 25 w
d.50 w
e. 200 w

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

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