5. Newton's Law of Cooling can be used to predict the temperature of a cooling liquid in a room that is at a certain steady temperature. We are going to model the temperature of a cooling cup of coffee. The Fahrenheit temperature of a cup of coffee, T, in a room that is at a 72 Fis given as a function of the number of minutes, m, it has been cooling by: T(m) =114(0.86)" + 72 (a) Find T(0) and using proper units, give a (b) What does the coefficient of 114 represent in terms of the situation being modeled? physical interpretation of your answer. (c) By what percent does the difference between the temperature of the coffee and the temperature of the room decrease cach minute? (d) I like my coffee when it is a nice temperature of around 100 F. How long should I wait?

5. Newton's Law of Cooling can be used to predict the temperature of a cooling liquid in a room that is at a certain steady temperature. We are going to model the temperature of a cooling cup of coffee. The Fahrenheit temperature of a cup of coffee, T, in a room that is at a 72 Fis given as a function of the number of minutes, m, it has been cooling by: T(m) =114(0.86)" + 72 (a) Find T(0) and using proper units, give a (b) What does the coefficient of 114 represent in terms of the situation being modeled? physical interpretation of your answer. (c) By what percent does the difference between the temperature of the coffee and the temperature of the room decrease cach minute? (d) I like my coffee when it is a nice temperature of around 100 F. How long should I wait?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Kinetic Theory of Gas

The Kinetic Theory of gases is a classical model of gases, according to which gases are composed of molecules/particles that are in random motion. While undergoing this random motion, kinetic energy in molecules can assume random velocity across all directions. It also says that the constituent particles/molecules undergo elastic collision, which means that the total kinetic energy remains constant before and after the collision. The average kinetic energy of the particles also determines the pressure of the gas.

P-V Diagram

A P-V diagram is a very important tool of the branch of physics known as thermodynamics, which is used to analyze the working and hence the efficiency of thermodynamic engines. As the name suggests, it is used to measure the changes in pressure (P) and volume (V) corresponding to the thermodynamic system under study. The P-V diagram is used as an indicator diagram to control the given thermodynamic system.

Question

5. Newton's Law of Cooling can be used to predict the temperature of a cooling liquid in a room that is at a
certain steady temperature. We are going to model the temperature of a cooling cup of coffee. The
Fahrenheit temperature of a cup of coffee, T, in a room that is at a 72°Fis given as a function of the number
of minutes, m, it has been cooling by:
T(m)=114(0.86)" + 72
(a) Find T(0) and using proper units, give a
(b) What does the coefficient of 114 represent in
terms of the situation being modeled?
physical interpretation of your answer.
(c) By what percent does the difference between
the temperature of the coffee and the
temperature of the room decrease each
minute?
(d) I like my coffee when it is a nice temperature
of around 100°F. How long should I wait?

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