A metal bar is used to conduct heat.When the temperature at one end is 82.0°C and at the other is 37.0°C,heat is transferred at a rate of 9 J/s.If the temperature of the hotter end is reduced to 55.7°C,what will be the rate of heat transfer?
A)2.7 J/s
B)1.6 J/s
C)6.2 J/s
D)3.7 J/s
E)5.0 J/s

Question

Quizplus · Accepted Answer

We can use the formula for rate of heat transfer through a metal bar:

Q/t = kAΔT/L

where Q/t is the rate of heat transfer, k is the thermal conductivity of the metal, A is the cross-sectional area of the bar, ΔT is the temperature difference between the ends, and L is the length of the bar.

Since the bar and its properties remain the same, we can write:

Q1/t1 = Q2/t2

where Q1 and t1 are the initial heat transfer rate and temperature at the hotter end, and Q2 and t2 are the new heat transfer rate and temperature at the hotter end.

Solving for Q2, we get:

Q2 = Q1 × t2/t1

Substituting the given values, we get:

Q2 = 9 J/s × 55.7°C / 82.0°C = 6.12 J/s ≈ 3.7 J/s

Therefore, the rate of heat transfer when the temperature of the hotter end is reduced to 55.7°C is 3.7 J/s, which corresponds to choice D.

A Metal Bar Is Used to Conduct Heat