The fundamental thermodynamic relation implies many thermodynamic identities that are valid in general, independent of the microscopic details of the system.
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In thermodynamics, "'Bridgman's thermodynamic equations "'are a basic set of thermodynamic equations, derived using a method of generating a large number of thermodynamic identities involving a number of thermodynamic quantities.
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Then according to the fundamental thermodynamic identity we have dE = T dS-P dV . If we keep the volume of the box constant, we have dS = dE / T = 4 a T ^ 2 dT . Integrating gives S = 4 / 3 a T ^ 3 = 4 / 3 E / T.
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