Читать книгу Geochemistry - William M. White - Страница 69

If the heat capacity of steam can be represented by a three-term power series:

with constants , , and , and the enthalpy of vaporization at 100°C is 40.6 kJ/mol, calculate the S and H changes when 1 mol of liquid water at 100°C and 1 atm is converted to steam and brought to 200°C and 3 atm. Assume that with respect to volume, steam behaves as an ideal gas (which, in reality, it is certainly not).

Answer: We need to calculate entropy and enthalpy associated with three changes: the conversion of water to steam, raising the steam from 100°C to 200°C, and increasing the pressure from 1 atm to 3 atm. Since both S and H are state variables, we can treat these three processes separately; our answer will be the sum of the result for each of these processes and will be independent of the order in which we do these calculations.

1 Conversion of water to steam. This process will result in ΔH of 40.6 kJ. For entropy, . We converted centigrade to Kelvin, or absolute, temperature.

2 Raising the steam from 100°C to 200°C (from 373 K to 473 K) isobarically. Since heat capacity is a function of temperature, we will have to integrate eqn. 2.112 over the temperature interval:Evaluating this, we find that . The entropy change is given by:Evaluating this, we find that .

3 Increasing pressure from 1 atm to 3 atm (0.1 MPa to 0.3 MPa) isothermally. We can use eqn. 2.114 to determine the enthalpy change associated with the pressure change. On the assumption of ideal gas behavior, we can substitute 1/T for α. Doing so, we find the equation goes to 0; thus, there is no enthalpy change associated with a pressure change for an ideal gas. This is in accord with assumptions about an ideal gas: namely, that there are no forces between molecules, hence no energy is stored as potential energy of attraction between molecules.

The isothermal pressure dependence of entropy is given by eqn. 2.106. We substitute 1/T for α and RT/P for V and integrate from P₁ to P₂:

The whole enthalpy and entropy changes are the sum of the changes in these three steps: