Question

(1)   What do you assume the entropy S for a perfect crystal when T = 0?

(2)   Is the S(0) still zero if the crystal is not perfect? Why?

(3)   How to calculate dS when under the constant pressure and c_p is given?

(4)   How to calculate the entropy of H₂O at 500 K?

(5)   How to calculate the entropy change for a chemical reaction if you can find the S for each chemical?

(6)   For an isolated thermodynamic system, dS ³ 0. That is, dS = 0 for a reversible process and dS > 0 for an irreversible process (spontaneous process).

Answer 1

1).The third law of thermodynamics is sometimes stated as follows, regarding the properties of closed systems in thermodynamic equilibrium:

The entropy of a system approaches a constant value as its temperature approaches absolute zero.

This constant value cannot depend on any other parameters characterizing the closed system, such as pressure or applied magnetic field. At absolute zero (zero kelvin) the system must be in a state with the minimum possible energy. Entropy is related to the number of accessible microstates, and there is typically one unique state (called the ground state) with minimum energy.In such a case, the entropy at absolute zero will be exactly zero. If the system does not have a well-defined order (if its order is glassy, for example), then there may remain some finite entropy as the system is brought to very low temperatures, either because the system becomes locked into a configuration with non-minimal energy or because the minimum energy state is non-unique. The constant value is called the residual entropy of the system. The entropy is essentially a state-function meaning the inherent value of different atoms, molecules, and other configurations of particles including subatomic or atomic material is defined by entropy, which can be discovered near 0 Kelvin.

2.At 0 K, the system is in its lowest energy state and there is only one way to distribute the energy, for a perfect crystal. So, they have zero entropy at absolute zero temperature. For an imperfect crystal, more than one "minimum energy states" are possible. ... This value of entropy is called the residual entropy.

3).Entropy is a state function. The entropy change is determined by its initial and final states only.In analyzing irreversible process, it is not necessary to make a direct analysis of actual reversible process.

Substitute actual process by an imaginary reversible process. The entropy change for imaginary reversible process is same as that of an irreversible process between given final and initial states.Q=∆H for constant pressure heating,

     

5).ΔS° for a reaction can be calculated from absolute entropy values using the same “products minus reactants” rule used to calculate ΔH°. Use the data in Table T2 to calculate ΔS° for the combustion reaction of liquid isooctane with O2(g) to give CO2(g) and H2O(g) at 298 K.