After heating up in a teapot, a cup of hot water is poured at a temperature of 207°F. The cup sits to cool in a room at a temperature of 72° F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below: T = Ta + (To – T.)e-kt Ta the temperature surrounding the object To = the initial temperature of the object t = the time in minutes the temperature of the object after t minutes k = decay constant T %3D The cup of water reaches the temperature of 193°F after 2 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 5 minutes. Enter only the final temperature into the input box.

Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter19: Temperature, Thermal Expansion And Gas Laws
Section19.1: Thermodynamics And Temperature
Problem 19.1CE: The Fahrenheit scale remains useful in part due to personal experience with temperature. For...
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After heating up in a teapot, a cup of hot water is poured at a temperature of 207°F.
The cup sits to cool in a room at a temperature of 72° F. Newton's Law of Cooling
explains that the temperature of the cup of water will decrease proportionally to the
difference between the temperature of the water and the temperature of the room, as
given by the formula below:
T = Ta+ (To - Ta)e kt
Ta
the temperature surrounding the object
То
the initial temperature of the object
%3D
t = the time in minutes
T = the temperature of the object after t minutes
k = decay constant
The cup of water reaches the temperature of 193°F after 2 minutes. Using this
information, find the value of k, to the nearest thousandth. Use the resulting
equation to determine the Fahrenheit temperature of the cup of water, to the
nearest degree, after 5 minutes.
Enter only the final temperature into the input box.
Transcribed Image Text:Watch help video After heating up in a teapot, a cup of hot water is poured at a temperature of 207°F. The cup sits to cool in a room at a temperature of 72° F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below: T = Ta+ (To - Ta)e kt Ta the temperature surrounding the object То the initial temperature of the object %3D t = the time in minutes T = the temperature of the object after t minutes k = decay constant The cup of water reaches the temperature of 193°F after 2 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 5 minutes. Enter only the final temperature into the input box.
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