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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider
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Blood plasma is stored at 400F. Before the plasma can be

Chapter 2, Problem 35E

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QUESTION:

Blood plasma is stored at 400F. Before the plasma can be used, it must be at 900F. When the plasma is placed in an oven at 1200F, it takes 45 min for the plasma to warm to 900F. Assume Newton’s law of cooling ( 34) applies. How long will it take for the plasma to warm to 900F if the oven temperature is set at (a) 1000F, (b) 1400F, and (c) 800F?

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QUESTION:

Blood plasma is stored at 400F. Before the plasma can be used, it must be at 900F. When the plasma is placed in an oven at 1200F, it takes 45 min for the plasma to warm to 900F. Assume Newton’s law of cooling ( 34) applies. How long will it take for the plasma to warm to 900F if the oven temperature is set at (a) 1000F, (b) 1400F, and (c) 800F?

ANSWER:

Solution:Step-1:a)In this problem we need to find the solution of the differential equation for T,and we have to find how long will it take for the plasma to warm to if the oven temperature is set at .The given differential equation is: .Here , M is the constant temperature , T is the temperature and k is the proportionality constant.Step-2:By using variable, separable method the differential equation can be written as:Integrate on both sides we get:, since - (-1) = 1, since ,here M is constant., since . , since is any constant.Step-3:Therefore, the solution of the dif

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