According to Stefan's law of radiation, the absolute temp. T of a body cooling in a medium at constant absolute temp. (T sub m) or Tm is given by:
dT/dt=k(T^4-T^4sub m) Solve the differential equation
dT/dt=k(T^4-T^4sub m) Solve the differential equation
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This is a variables separable first order differential equation.
dT/dt = k(T^4 - Tm^4) ----> INT dT/(T^4 - Tm^4) = INT k dt
Integrate each side separately. You will need to split the left side into partial fractions.
A/(T - Tm) + B/(T + Tm) + CT/(T^2 + Tm^2) + D/(T^2 + Tm^2)
Can you finish from there? Remember that Tm is a constant. The first three terms on the left will integrate to natural logarithms and the fourth to arctan.
dT/dt = k(T^4 - Tm^4) ----> INT dT/(T^4 - Tm^4) = INT k dt
Integrate each side separately. You will need to split the left side into partial fractions.
A/(T - Tm) + B/(T + Tm) + CT/(T^2 + Tm^2) + D/(T^2 + Tm^2)
Can you finish from there? Remember that Tm is a constant. The first three terms on the left will integrate to natural logarithms and the fourth to arctan.
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Could you tell me if this is right? I got A ln(t)+Bln(t)+Cln(t)/2+1/T^2m[t… (T/Tm)]=kt+C....
then I divided both sides by t (basically just put all that over t)....is this my final answer k=this answer?
then I divided both sides by t (basically just put all that over t)....is this my final answer k=this answer?
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