q1) q2) Newton\'s law of cooling states that the temperature of an object change
ID: 2838051 • Letter: Q
Question
q1)
q2)
Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. The coffee has a temperature of 210 degrees Fahrenheit when freshly poured, and 1.5 minutes later has cooled to 198 degrees in a room at 72 degrees. a) What is the temperature after 3 minutes? b) Determine when the coffee reaches a temperature of 148 degrees The coffee will reach a temperature of 148 degrees in minutesExplanation / Answer
1)a)dT/dt=-k(T-T0)
T=T0+(Ti-T0)e^(-kt)
Substituting values to find k.
198=72+(210-72)e^(-k*1.5)
k=0.060648
T(3)=72+(210-72)e^(-0.060648*3)=187F
b)148=72+(210-72)e^(-0.060648*t)
t=9.84min
2a)k=ln(2)/t1/2=ln(2)/15=0.04621/day
Q(t)=Q0e^-kt=250e^(-0.04621t)
b)Q(39)=250e^(-0.04621*39)=41.2mg
c)1=250e^(-0.04621t)
t=119.5 days
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