Newton in his studies discovered that the rate of cooling of an object could be
ID: 2970444 • Letter: N
Question
Newton in his studies discovered that the rate of cooling of an object could be approximated by the difference in temperature of the object and its surroundings. If the temperature of the surroundings is a constant 65 degrees F, the proportionality constant k=0.01 and a coffee cup is poured at 175 degrees F.
A) write the differential equation and estimate the temperature of the coffee after 2 minutes using 4 steps of euler's method
B) solve the differential equation and find the exact value after 2 minutes.
Explanation / Answer
A)-dT/dt=0.01(T-65)
step size=0.5 minutes
w(0)=T(0)=175
w1=w0+0.5(-0.01w0+0.65)=174.775
w2=w1+0.5(-0.01w1+0.65)=174.226
w3=w2+0.5(-0.01w2+0.65)=173.67
y(2)=w4=w3+0.5(-0.01w3+0.65)=173.12
b)Integrating the differential ekuation:
ln(T-65)=-0.01t+c
At t=0 T=175
so ln (110)=c
=>ln[(T-65)/110]=-0.01t
=>T=65+110*e^-0.02=172.82