Hello, I have a Mat Lab project with the following task: examine what happens to a building in the winter when the heat goes out. There are three important equations:

(1) Q = Dt * (A*(T2 T1 )/R)

where: Q is the change in heat (BTU British Thermal Unit)

Dt is the amount of time over which the heat is being lost (hours)

A is the exterior surface area of the building (ft^2)

T2 is the initial interior temperature (). This changes over time.

T1 is the exterior temperature (). This changes based on Equation 3, below. (Note that T2 T1 is the difference between the internal external temperatures and is not a change like T, seen below.)

R is the thermal resistance of the walls (called the R-value) (*ft2*hour/BTU)

(2) DT = Q/Ctm*Mt

where: Q is the change in heat within the building (BTU)

DT is the change in internal temperature () over time Dt

Mt is the thermal mass of the building (lb)

Ctm is the average heat coefficient of the building material use 0.35BTU/(lb)

(3) T1 = 10 10 cos (( t * pi) / 12))

where: T1 is the exterior temperature ().

t is the time (hours)

Write a function that takes the initial interior temperature as an input and plots the internal temperature for a period of 72 hours. Other parameters should be hard-wired into the function. Your function should produce a labeled plot of internal temperature vs. time. A normal small house has a thermal mass of around 20,000 lbs. R-value is 15 to 40*ft2*hour/BTU. Your house has a footprint = 10*sum(my_name) and 9 ft tall walls. Assume your house is square. Dont forget to include the roof in your surface area (but not the floor well assume the ground is reasonably warm). This is a time stepping problem, meaning you will need to choose a value for Dt.

Goal:

-Create the function

-An instance of your function running for the mass and R-value

-A labeled plot of temperature versus time

This is what I have so far:

function T2_2 = temperature_calculator (T1,T2) R=10*sum('David')*9; R=15; A= 5*R; Dt= 1/72; Q=Dt*(A*(T2-T1)/R); Mt=20;000; Ctm=0.35; DT = Q/Ctm*Mt; t= 1; T1=10-10*cos((t*pi)/12); for i=1

Thank you!