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A thin bar composed of aluminum is 20 cm long. It is initially at a uniform temperature of 30° C. At time t = 0, the left end of the bar (x = 0) is placed in a bath at a constant temperature of 20° C. The right end of the bar (x = 20 cm) is placed in a bath kept at a constant 40° C. (a) Derive the temperature function of the bar for any point in the bar at any time. How does the temperature at the center of the bar change with time?

A thin bar composed of aluminum is 20 cm long. It is initially at a uniform temperature of 30° C. At time t = 0, the left end of the bar (x = 0) is placed in a bath at a constant temperature of 20° C. The right end of the bar (x = 20 cm) is placed in a bath kept at a constant 40° C. (a) Derive the temperature function of the bar for any point in the bar at any time. How does the temperature at the center of the bar change with time?

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 57SE: Repeat the previous exercise to find the formula forthe APY of an account that compounds daily....
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A thin bar composed of aluminum is 20 cm long. It is initially at a uniform temperature of 30° C. At time t = 0, the left end of the bar (x = 0) is placed in a bath at a constant temperature of 20° C. The right end of the bar (x : constant 40° C. 20 cm) is placed in a bath kept at a (a) Derive the temperature function of the bar for any point in the bar at any time. How does the temperature at the center of the bar change with time?
Transcribed Image Text:A thin bar composed of aluminum is 20 cm long. It is initially at a uniform temperature of 30° C. At time t = 0, the left end of the bar (x = 0) is placed in a bath at a constant temperature of 20° C. The right end of the bar (x : constant 40° C. 20 cm) is placed in a bath kept at a (a) Derive the temperature function of the bar for any point in the bar at any time. How does the temperature at the center of the bar change with time?
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