Question
I don't believe my answer is correct... can anyone help? 1. Newton's Law of Cooling. According to Newton's law of cooling, if an object at
I don't believe my answer is correct... can anyone help?
1.Newton's Law of Cooling. According to Newton's law of cooling, if an object at temperature T is immersed in a medium having the constant temperature M, then the rate of change of T is proportional to the difference of temperature MT. This gives the differential equation
dT/dt = k(M - T)
a.Solve the differential equation for T..
dT/dt = k(M - T)
dt[dT/dt = k(M - T)]
dT = k(M - T) dt
[dT = k(M - T) dt] 1/(M - T)
1/(M - T) dT = k dt
1/(M - T) dT = k dt
1/(M - T) dT = k dt
Ln |M - T| = kt
eLn |M - T| = ekt
|M - T| = ekt
|M| - |T| = ekt
- |T| = ekt - |M|
T = M - ekt + C where M - T 0 or M T and M and T are positive real numbers (hence, the absolute value).
b.A thermometer reading 100F is placed in a medium having a constant temperature of 70F. After 6 min, the thermometer reads 80F. What is the reading after 20 min?
T = 100; M = 70; t = 0; k = 0;
T(0) = 100
100 = 70 - ek(0) + C
100 = 70 - e0 + C
100 = 70 - 1 + C
100 = 69 + C
31 = C
M = 70; t = 6; k = 20; C = 31
T(6) = ?, what's T?
|T| = |M| - ekt + C
|T| = (|70| - e(20)(6)) + 31
|T| = 70 - e120 + 31
|T| = 101 - e120
T = .
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