 Entropy gain from impact and thermal equilibration

ID: entropy-gain-from-impact-and-thermal-equilibration

A body of mass

m

c

T_{i}

v

that stops in a large reservoir at

T_{L}

produces entropy

m c [lo g (T_{L} / T_{i}) + T_{i} / T_{L} - 1] + m v^{2} / (2 T_{L})

, assuming constant heat capacity and no phase changes. The first term follows by adding the body's logarithmic entropy change to the reservoir's heat gain; the second is kinetic-energy dissipation. A numerical answer needs the reservoir temperature.

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