Question

Your friend was tasked with bringing the drinks to the tailgate party, but they forgot and left the drinks in their car and it was over 90 degrees outside and the drinks are really warm. You are going to help your friend determine how long it will take to cool the drinks by writing some code. You know Newton's Law of Cooling tells the temperature of an object (T) as a function of time given it's initial temperature (T) and it's current environment's temperature (T) as follows: T.-T.: (T. - T)ekt, where k is an energy constant (k-0.35). Let's write some code: A. Create 3 input statements that ask for (1) the current temperature of the drinks in "F, (2) the temperature of your friend's fridge in "F, and (3) your favorite drinking temperature in "E. B. Calculate the time, t(units of hours), required to cool the drinks based on the Newton's Law of Cooling D. Write output statements that report the time needed:example: It should take <t> hours to cool the drinks to <Tl> degrees F if my fridge has a temperature of <T2 > degrees F) E. Create a time vector, starting with zero and ending with a time that is twice the minutes you calculated in part B. Choose an increment or a number of data points that makes a reasonable plot. Plot the drink temperature Te as a function of time. Make sure you add a plot title, axis titles and use a red line with diamond markers.

The second photo is what the Instructor gave us to start off with. You are able to select what you want when it comes to the “T”s but nothing to over exaggerated.

Answer 1

clc;
% Matlab script to calculate the time required to cool the drinks and then
% plot the cooling temperature vs time
% inputs
Ti = input('Enter the current temperature of the drinks (in F) : ');
Tr = input('Enter the temperature of the fridge (in F) :');
Tc = input('Enter your favorite drinking temperature (in F) : ');
k = 0.35;
% calculate the time required
t = log((Tc-Tr)/(Ti-Tr))/(-k);
fprintf('It should take %.2f hours to cool the drinks to %.2f degrees F if my fridge has a temperature of %.2f degrees F',t,Tc,Tr);
% create a time vector
time = (0:0.25:2*t);
% calculate the cooling temperature for the different time values
Tnc = Tr+(Ti-Tr) .* exp( -k.* time );
% plot the graph
plot(time,Tnc,'rd-');
title('Drink Temperature v/s Time');
xlabel('Time');
ylabel('Drink temperature');
%end of script

Output:

Enter the current temperature of the drinks (in F) 120 Enter the temperature of the fridge (in F) 60 Enter your favorite drinking temperature (in F) 45 It should take 3.96 hours to cool the drinks to 45.00 degrees F if my fridge has a temperature of 60.00 degrees F Figure 1 X File Edit View Insert Iools Desktop Window Help Drink Temperature v/s Time 120 110 100 90 80 70 60 0 3 6 1 2 4 5 7 8 Time E68B 8 Drink temperature