From: "JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439" <JLU@hep.anl.gov>
Date: Mon, 9 Dec 1996 11:14:22 -0600 (CST)
Hi Ludwik-
No mistake. Proportional to t for short times. You write:
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Let me try. I assume that initially t=0 and T=T_i. If T>>T_0 then
dT/dt=-k*T^4 or dT/(T^4)=-k*dt. I integrate and get
(1/T_i^3 - 1/T^3) = -3*k*t or 1/T^3 = (1/T_i^3 + 3kt)
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So solve for T to get:
T = T_i(1+3ktT_i^3)^-1/3
For sufficiently short times this is well-approximated by
T = T_i(1 - 3ktT_i^3),
which is a decrease proportional to t.