Entropy

In astrophysics, what is referred to as "entropy" is actually the adiabatic constant derived as follows. Using the first law of thermodynamics for a quasi-static, infinitesimal process for a hydrostatic system For an ideal gas in this special case, the internal energy, U, is only a function of the temperature T; therefore the partial derivative of heat capacity with respect to T is identically the same as the full derivative, yielding through some manipulation Further manipulation using the differential version of the ideal gas law, the previous equation, and assuming constant pressure, one finds