The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of (2), given in Section 3.1, is dT dt = KS(T - Tm), where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 66° C. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 37° C. If Tm = 21° C, then what is the temperature of the coffee in cup B after 30 min? (Round your answer to two decimal places.) °C
The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of (2), given in Section 3.1, is dT dt = KS(T - Tm), where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 66° C. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 37° C. If Tm = 21° C, then what is the temperature of the coffee in cup B after 30 min? (Round your answer to two decimal places.) °C
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 at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of (2),
given in Section 3.1, is
KS(T-Tm),
where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the
temperature of the coffee is 66° C. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in
cup A. After 30 min the temperature of the coffee in cup A is 37° C. If Tm = 21° C, then what is the temperature of the
coffee in cup B after 30 min? (Round your answer to two decimal places.)
°C
dT
dt
=
Expert Solution
Step 1
The Rate at which a body cools down is given by,
where k < 0 and is a constant.
Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is .
The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A.
After 30 min the temperature of the coffee in cup A is . If ,
To Find: The temperature of the coffee in cup B after 30 min.
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