Measurement of the rates of evaporation of amorphous water (a) and ice (i) near 150 K can be interpreted as giving a measure of their free energy difference, Delta(i)(a)G (150 K) = 1100+/-100 J/mol, which, together with the known enthalpy difference and heat capacity data, suggests a residual entropy difference of Delta(i)(a)S (0) = -0.7+/-2.2 J/(K mol) at absolute zero. Previous theoretical estimates of Delta(i)(a)S (0), which are much larger, did not allow the amorph to be connected with normal liquid water by a reversible thermodynamic path at atmospheric pressure. The present value allows such a connection.