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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
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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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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