The entropy of a thermal reservoir of unknown temperature is defined by the function (S=a E^{3} /
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The entropy of a thermal reservoir of unknown temperature is defined by the function \(S=a E^{3} / 3 b^{2}\).
(a) Derive an expression for the entropy gradient \(d S / d E\).
(b) Calculate the entropy gradient of the reservoir if the ratio \(E / b\) is \(3.00 \mathrm{~J}^{-1}\) and \(a=1.00 \mathrm{~J}\).
(c) Find the temperature of the reservoir.
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