Estimating absolute entropy

Question

The heat capacity, , of liquid carbon disulfide is a relatively constant  . However, the heat capacity of solid carbon disulfide varies greatly with temperature. From  to its melting point at  , the heat capacity of solid carbon disulfide increases linearly from  to  .

The enthalpy of fusion of carbon disulfide is  . 

The absolute entropy of liquid carbon disulfide at  is  .

Estimate the absolute entropy of carbon disulfide at  .

Answer 1

Hi Danielle J.,

.So divide both sides by T, then integrate with respect to T. That will give you the portions NOT related to the melt (you can do this graphically, or by calculus). Since for the melt, at the melt temperature, .delta.G = 0 (it's in equilibrium), then .delta.H = T.delta.S . So that gives you .delta.S for the melt. Put all together for .delta.S, and then subtract that from the given value for the liquid.

The thing to remember here is that Cp (in addition to being heat capacity, experimentally) is a proportioning constant between temperature T and the rate of change of entropy with respect to temperature (partial.delta.S/partial.delta.T). Thus, even if Cp were constant across a range of temperature, as T increases, the incremental increases in S become smaller and smaller for every degree hotter. Think about that for a while, and turn it over in your head, to get an intuitive "feel" for entropy: as you feed ever more heat in, you are getting less bang for your buck at increasing entropy -- I like to think of it as, the system is already disordered by the heat, so you can't disorder it further as effectively, even by heating it up further.

-- Cheers, -- Mr. d..