   Chapter 11, Problem 55AP

Chapter
Section
Textbook Problem

The bottom of a copper kettle has a 10.0-cm radius and is 2.00 mm thick. The temperature of the outside surface is 102°C, and the water inside the kettle is boiling at 1 atm of pressure. Find the rate at which energy is being transferred through the bottom of the kettle.

To determine
The rate at which energy is being transferred through the bottom of the kettle.

Explanation

Given Info: Radius of the bottom of the copper kettle 10.0cm , thickness is 2.00mm Temperature outside the surface is 102°C , and the water inside the kettle is boiling at 1 atm of pressure, the thermal conductivity of copper is 397W/m°C .

Formula to find rate at which energy is being transferred through the bottom of the kettle.

P=kA(ThTc)L

• P is rate at which energy is being transferred through the bottom of the kettle.
• k is thermal coefficient of copper.
• A is the bottom area of the kettle.
• Th is the higher temperature.
• Tc is the lower temperature.
• L is the thickness of the flask.

The formula for the area of the circle is,

A=πr2

• r is the radius of the bottom area of the kettle.

Use πr2 for A in the rate at which energy is being transferred equation.

P=k(πr2)(ThTc)L

At 1 atm pressure the temperature at which the water boils is 100°C .

Substitute 397W/m°C for k , 10.0 cm for r, 102°C for Th , 100°C for Tc , and 2

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