The rate of cooling a metal ball can be expressed as dT 3D - k(Т — Та) dt Where T= temperature of the metal ball (C), Ta= temperature of water (C), t = time (min) and k= the proportionality constant (min-!). A metal ball at initial temperature of 90 °C is dropped into water reservoir that is held at a constant value of Ta= 15 °C. Estimate how long it takes the ball to cool to less than 40 °C if k= 0.2 min-1.
The rate of cooling a metal ball can be expressed as dT 3D - k(Т — Та) dt Where T= temperature of the metal ball (C), Ta= temperature of water (C), t = time (min) and k= the proportionality constant (min-!). A metal ball at initial temperature of 90 °C is dropped into water reservoir that is held at a constant value of Ta= 15 °C. Estimate how long it takes the ball to cool to less than 40 °C if k= 0.2 min-1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The rate of cooling a metal ball can be expressed as
dT
3D - k(Т — Та)
dt
Where T= temperature of the metal ball (C), Ta= temperature of water (C), t = time (min) and
k= the proportionality constant (min-!). A metal ball at initial temperature of 90 °C is dropped into
water reservoir that is held at a constant value of Ta= 15 °C. Estimate how long it takes the ball
to cool to less than 40 °C if k= 0.2 min-1.
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