Let an isolated system be composed of one part at T1 and a second part at T2, with T2, > T1; let the parts be separated by a wall that allows heat flow at only an infinitesimal rate. Show that, when heat dq flows irreversibly from T2, to T1, we have dS = dq/T1 − dq/T2 (which is positive). (Hint: Use two heat reservoirs to carry out the change of state reversibly.)
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