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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), T, = temperature of water (°C), t = time (min) and k= the proportionality constant (min-1). A metal ball at initial temperature of 90 °C is dropped into water reservoir that is held at a constant value of T, = 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), T, = temperature of water (°C), t = time (min) and k= the proportionality constant (min-1). A metal ball at initial temperature of 90 °C is dropped into water reservoir that is held at a constant value of T, = 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
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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The rate of cooling a metal ball can be expressed as dT dt -k(T – Ta) Where T = temperature of the metal ball (°C), To = temperature of water (°C), t = time (min) and k= the proportionality constant (min-1). A metal ball at initial temperature of 90 °C is dropped into water reservoir that is held at a constant value of T, = 15 °C. Estimate how long it takes the ball to cool to less than 40 °C if k = 0.2 min-1
Transcribed Image Text:The rate of cooling a metal ball can be expressed as dT dt -k(T – Ta) Where T = temperature of the metal ball (°C), To = temperature of water (°C), t = time (min) and k= the proportionality constant (min-1). A metal ball at initial temperature of 90 °C is dropped into water reservoir that is held at a constant value of T, = 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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