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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.7: Applied Problems
Problem 68E
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3.2.7

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 =
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,

dTdt=kST-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,

To Find: The temperature of the coffee in cup B after 30 min.

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