Stefan\'s Law of Radiation states that the rate of change in temperature of a bo

Question

Stefan's Law of Radiation states that the rate of change in temperature of a body at T(t) degrees in a medium at M(t) degrees is proportional to M^4 - T^4. That is, dT/dt= K*[M(t)^4 - T(t)^4] ; where K is a constant. Let K = (40)^-4 and assume that the medium temperature is constant, M(t) = 70. If T(0) = 100, use Euler's method with h = :1 to approximate T(1) and T(2). What do you get if h = :01? I am really confused on how to initially start this problem. Can someone please show me how to start this problem so I can figure this one out. I understand how to perform Euler's method, I just don't know how to start this specific problem. They have the solution to this problem on here. It's problem 16 on chapter 1.4 of the book Fundamentals of Differential Equations Eighth Edition by Nagle, Saff, and Snider. But the on here skips the initial steps. Please show those steps so I know how to move on. Thank you.

Explanation / Answer

Dear stefen's law is
the energy emitted or gained by a body per unit area in per unit time(what's called intensity) is directly proportional to the difference of the fourth power of temperature of each and also on emittance of object.
Or

intensity=sigma*e* T^4-M^4

e is emittance of body.
since T>M
intensity will be positive showing heat will be lost by the body.

Emittance or e or .25 is given both temperature given and sigma is a constant for value concern book i think its 2.567 likewise.

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