   Chapter 11, Problem 75AP

Chapter
Section
Textbook Problem

An aluminum rod and an iron rod are joined end to end in good thermal contact. The two rods have equal lengths and radii. The free end of the aluminum rod is maintained at a temperature of 100.°C, and the free end of the iron rod is maintained at 0°C. (a) Determine the temperature of the interface between the two rods. (b) If each rod is 15 cm long and each has a cross-sectional area of 5.0 cm2, what quantity of energy is conducted across the combination in 30. min?

(a)

To determine
The temperature of the interface between two rods.

Explanation

Given info: Two rod have equal length and radii, the free end of aluminum rod is at 100°C and free end of aluminum rod is at 0°C .

Formula to calculate the rate at which energy transferred for aluminum rod is,

PAl=kAlA(TAlT)L

• PAl is the rate of energy transfer across the aluminum rod,
• kAl is the thermal conductivity of aluminum rod,
• A is the area of the rod,
• TAl is temperature of the free end of aluminum rod,
• T is temperature at the interface between two rods,
• L is the length of the rod,

Formula to calculate the rate at which energy transferred for iron rod is,

PFe=kFeA(TTFe)L

• PFe is the rate of energy transfer across the iron rod,
• kFe is the thermal conductivity of iron rod,
• TFe is temperature of the free end of iron rod,

Energy transfer for each of the rods is same in steady state.

Equate both the rate of energy transfer equations and rewrite it in terms of T.

kAlA(TAlT)L=kFeA(TTFe)LkAl(TAlT)=kFe(TTFe)kAlT+kFe

(b)

To determine
The quantity of energy conducted across the rods.

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