a. Explanation Proof: Given: An object with an initial temperature of T 0 > 0 is put in the surroundings with an ambient temperature of A where A < T 0 2 and t 1 2 is the time required for the object to cool to T 0 2 . Calculation: Since the problem is dealing with cooling, use the Newton’s law of cooling. The general solution for Newton’s law of cooling can be written as T ( t ) = ( T 0 − A ) e − k t + A . The time required for the object to cool to T 0 2 is t 1 2 . That is, the initial condition T ( t 1 2 ) = T 0 2 . Apply the initial condition on the above cooling equation T ( t ) = ( T 0 − A ) e − k t + A . That is, T 0 2 = ( T 0 − A ) e − k t 1 2 + A T 0 2 − A = ( T 0 < b . To determine To explain: Whether the cooling time t 1 2 is increase or decrease with respect to increase the value of k . c . To determine To explain: The required condition on A < T 0 2 .

2nd Edition

ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

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Chapter D1.4, Problem 38E

To determine

To show: t12=−1kln[T0−2A2(T0−A)]

To determine

To explain: Whether the cooling time t12 is increase or decrease with respect to increase the value of k.

To determine

To explain: The required condition on A<T02 .

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Chapter D1.4, Problem 37E

Chapter D1.4, Problem 39E

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t 1 2 = − 1 k ln [ T 0 − 2 A 2 ( T 0 − A ) ]

Solution Summary: The author explains the Newton's law of cooling and how to calculate the time required for the object to cool to T_02.

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To show: t12=−1kln[T0−2A2(T0−A)]

To explain: Whether the cooling time t12 is increase or decrease with respect to increase the value of k.

To explain: The required condition on A<T02 .

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