Question
A body of an unknown temperature was placed in a room that was held at 30°F. After 10 minutes, the body's temperature was 0°F, and 20 minutes after the body was placed in the room the body's temperature was 15°F. Estimate the body's initial temperature.
Thank you!!
Thank you!!
Answers
Damon
I am going to assume that the heat flow into the body is proportional to the difference between body temp T and 30 and rate of change of T is proportional to heat flow .
dT/dt = k (30-T)
try T = -ae^-kt + 30
that is 30 at t-->oo and 30-a at t = 0
so
0 = -a e^-10k + 30
15= -a e^-20k + 30
30 = a e^-10k
45 = a e^-20 k
a = 30/e^-10k
45 = 30 (e^-20k/e^-10k)
45/30 = e^-10k
I think you can take it from there, check arithmetic
dT/dt = k (30-T)
try T = -ae^-kt + 30
that is 30 at t-->oo and 30-a at t = 0
so
0 = -a e^-10k + 30
15= -a e^-20k + 30
30 = a e^-10k
45 = a e^-20 k
a = 30/e^-10k
45 = 30 (e^-20k/e^-10k)
45/30 = e^-10k
I think you can take it from there, check arithmetic
alv
the 8th line is the simplification of the sixth line,,, im wandering why it is 45? is the algebraic solution wrong?