   Chapter 11, Problem 45P

Chapter
Section
Textbook Problem

A steam pipe is covered with 1.50-cm-thick insulating material of thermal conductivity 0.200 cal/cm · °C · s. How much energy is lost every second when the steam is at 200.°C and the surrounding air is at 20.0°C? The pipe has a circumference of 800. cm and a length of 50.0 m. Neglect losses through the ends of the pipe.

To determine
The amount of energy lost every second.

Explanation

Given info: The thickness of the pipe is 1.50 cm, thermal conductivity of insulating material is 0.200cal/cm°Cs , temperature of the steam is 200°C , temperature of the surrounding air is at 20.0°C , the circumference of the pipe is 800 cm and its length is 50.0 m.

Formula to calculate the rate at which energy is transferred is,

P=kA(ThTc)L

• P is the rate of energy transfer,
• k is the thermal conductivity of insulating material,
• Th is temperature of the steam,
• Tc is temperature of the surrounding,
• L is the thickness of the pipe,
• A is the surface area of the pipe,

Formula to calculate the surface area of the pipe is,

A=Cl

• C is the circumference of the pipe,
• l is the length of the pipe,

Use Cl for l in P=kA(ThTc)L to rewrite P .

P=k(Cl)(ThTc)L

Substitute 0.200cal/cm°Cs for k, 1

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