The derivative of this quantity with respect to temperature is the negative of the entropy.
The derivative of this quantity with respect to temperature is the negative of the entropy. This quantity, whose natural variables are temperature and pressure, is proportional to the logarithm of the equilibrium constant. Chemical equilibrium is attained when this quantity is minimized and it is constant along a coexistence curve. A reaction will occur spontaneously if the change in this quantity is negative. Enthalpy minus temperature times entropy is equal to this quantity. For 10 points, name this measure of the amount of  energy in a system available for useful work, named for an American scientist.
The derivative of this quantity with respect to temperature is the negative of the entropy.
{Gibbs free energy} [accept {Gibbs energy}, {Gibbs function} or {free enthalpy}; prompt on partial answer]