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After sitting on a shelf for a while, a can of soda at a room temperature (69°F) s placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 37°F. Newton's Law of Cooling explains that the temperature of the can of soda will decrease proportionally to the difference between the emperature of the can of soda and the temperature of the refrigerator, as given by the formula below: T = Ta + (To – Ta)e-kt

After sitting on a shelf for a while, a can of soda at a room temperature (69°F) s placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 37°F. Newton's Law of Cooling explains that the temperature of the can of soda will decrease proportionally to the difference between the emperature of the can of soda and the temperature of the refrigerator, as given by the formula below: T = Ta + (To – Ta)e-kt

Chemistry: Principles and Practice
Chemistry: Principles and Practice
3rd Edition
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Chapter5: Thermochemistry
Section: Chapter Questions
Problem 5.101QE: In the 1880s, Frederick Trouton noted that the enthalpy of vaporization of 1 mol pure liquid is...
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After sitting on a shelf for a while, a can of soda at a room temperature (69°F) is placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 37°F. Newton's Law of Cooling explains that the temperature of the can of soda will decrease proportionally to the difference between the temperature of the can of soda and the temperature of the refrigerator, as given by the formula below: T = Ta + (To – Ta)e¬kt 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 The can of soda reaches the temperature of 54°F after 40 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the can of soda, to the nearest degree, after 95 minutes. Enter only the final temperature into the input box.
Transcribed Image Text:After sitting on a shelf for a while, a can of soda at a room temperature (69°F) is placed inside a refrigerator and slowly cools. The temperature of the refrigerator is 37°F. Newton's Law of Cooling explains that the temperature of the can of soda will decrease proportionally to the difference between the temperature of the can of soda and the temperature of the refrigerator, as given by the formula below: T = Ta + (To – Ta)e¬kt 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 The can of soda reaches the temperature of 54°F after 40 minutes. Using this information, find the value of k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the can of soda, to the nearest degree, after 95 minutes. Enter only the final temperature into the input box.
Expert Solution
Step 1

Given:

Ta = the temperature surrounding the object = temp. of refrigerator = 37oF

To = initial temperature of the object =temp. of can soda when kept in room =  69oF

T = temperature of object after t minutes = 54oF

t = the time in minutes = 40 minutes

k = decay constant

To calculate:

1. k, for the above data.

2. Temp. after 95 minutes, T

 

 

 

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