The water temperature T in a tank takes 20 minutes to decrease from 100°C to 60°C. The temperature of the surrounding air is kept constant at To = 23°C. a) Assuming that the rate of temperature decrease is proportional to the difference of current water temperature and constant air temperature, find the differential equation describing water temperature as a function of time. b) Solve the differential equation subject to the initial condition. c) Find the coefficient of proportionality and relaxation time of temperature.
The water temperature T in a tank takes 20 minutes to decrease from 100°C to 60°C. The temperature of the surrounding air is kept constant at To = 23°C. a) Assuming that the rate of temperature decrease is proportional to the difference of current water temperature and constant air temperature, find the differential equation describing water temperature as a function of time. b) Solve the differential equation subject to the initial condition. c) Find the coefficient of proportionality and relaxation time of temperature.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:The water temperature T in a tank takes 20 minutes to decrease from 100°C to 60°C. The
temperature of the surrounding air is kept constant at To=23°C.
a) Assuming that the rate of temperature decrease is proportional to the difference of current
water temperature and constant air temperature, find the differential equation describing
water temperature as a function of time.
b) Solve the differential equation subject to the initial condition.
c) Find the coefficient of proportionality and relaxation time of temperature.
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