Explanation Given: The blood plasma is stored at 40 ° F . Before the use of plasma it must be at 90 ° F . The oven temperature is 120 ° F . Calculation: Consider the Newton’s law of cooling. d T d t = k ( M − T ) d T d t = − k ( T − M ) Separate the variable as follows. d T ( T − M ) = − k d t Integrate both the sides of above equation as follows. ∫ d T ( T − M ) = ∫ − k d t ln ( T − M ) = − k t + C 1 ( T − M ) = e − k t e C 1 T = M + C e − k t … ( 1 ) Here, M is temperature of surrounding, and T is the temperature of the object. Substitute 40 ° F for T , 0 for t , and 120 ° F for M in equation ( 1 ) to obtain the value of C . 40 = 120 + C e − k ( 0 ) C = 40 − 120 = − 80 Substitute − 80 for C in equation ( 1 ) . T = M − 80 e − k t … ( 2 ) Given that after 45 minutes plasma warm up to 90 ° F . Substitute 90 ° F for T , 45 minutes for t , and 120 ° F for M in equation ( 2 ) to obtain the value of k . 90 = 120 − 80 e − k ( 45 ) − 80 e − k ( 45 ) = − 30 e − k ( 45 ) = 3 8 Take ln on both sides as follows, To determine b) To find: The time at which the plasma is warm to 90 ° F if the oven temperature is 140 ° F . To determine c) To find: The time at which the plasma is warm to 90 ° F if the oven temperature is 80 ° F .

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 2.2, Problem 35E

To determine

a)

To find:

The time at which the plasma is warm to 90° F if the oven temperature is 100° F.

To determine

b)

To find:

The time at which the plasma is warm to 90° F if the oven temperature is 140° F.

To determine

c)

To find:

The time at which the plasma is warm to 90° F if the oven temperature is 80° F.

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Chapter 2.2, Problem 34E

Chapter 2.2, Problem 36E

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Fundamentals of Differential Equations and Boundary Value Problems

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a) To find: The time at which the plasma is warm to 90 ° F if the oven temperature is 100 ° F .

Solution Summary: The author explains how to find the time at which the plasma is warm if the oven temperature is 100°.

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a)

To find:

The time at which the plasma is warm to 90° F if the oven temperature is 100° F.

b)

To find:

The time at which the plasma is warm to 90° F if the oven temperature is 140° F.

c)

To find:

The time at which the plasma is warm to 90° F if the oven temperature is 80° F.

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Chapter 2 Solutions

a) To find: The time at which the plasma is warm to 90 ° F if the oven temperature is 100 ° ​ ​ F .

Solution Summary: The author explains how to find the time at which the plasma is warm if the oven temperature is 100°.

Concept explainers

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a) To find: The time at which the plasma is warm to 90° F if the oven temperature is 100° ​​F.

b) To find: The time at which the plasma is warm to 90° F if the oven temperature is 140°​ F.

c) To find: The time at which the plasma is warm to 90° F if the oven temperature is 80° F.

Want to see the full answer?

Chapter 2 Solutions

a) To find: The time at which the plasma is warm to 90 ° F if the oven temperature is 100 ° F .

a)

To find:

The time at which the plasma is warm to 90° F if the oven temperature is 100° F.

b)

To find:

The time at which the plasma is warm to 90° F if the oven temperature is 140° F.

c)

To find:

The time at which the plasma is warm to 90° F if the oven temperature is 80° F.