Question
When water changes from the liquid phase to the gaseous (vapor) phase, energy is required for the H2O molecules to escape their mutual molecular attraction (the internal energy change ufg in the steam...
When water changes from the liquid phase to the gaseous (vapor) phase, energy is required for the H2O molecules to escape their mutual molecular attraction (the internal energy change ufg in the steam tables) and for the volume expansion (P·vfg). The total heat of vaporization for the phase change is represented by the enthalpy change hfg in the steam tables. Use the steam tables to calculate the fractions of energy for the volume expansion and for the molecules to escape their mutual attraction at P = 0.1 and 0.2 MPa respectively. What conclusion may be drawn with respect to the effect of the pressure?
Answers
The energy required for vaporization of water is expressed as the enthalpy of vaporization (ΔHv). According to the definition of enthalpy:
Where:
H is the enthalpy
U is the internal energy
P is the pressure of the system
V is the volume of the system
For a change of enthalpy in a vaporization process, equation (1) is rewritten as:
At constant pressure, we have;
Using steam tables for a given pressure value, we can know the values of the enthalpy of vaporization, the change in internal energy and the change in volume between the gas and liquid phase during a vaporization process.
At pressure of P = 0.1 MPa, we have:
The change in internal energy is required for the molecules to escape to their mutual molecular attraction. The fraction of this energy respect to the heat of vaporization is given by the quotient:
If we divide equation (2) by the heat of vaporization:
Then, the fraction of energy required by the volume expansion is:
At pressure of P = 0.2 MPa, we have:
The fraction of energy required by the change in internal energy is:
Then, the fraction of energy required by the volume expansion is:
As a conclusion, we can see that pressure increases the fraction of energy required in the volume expansion respect to the total vaporization heat. It is clearly visible in equation (2), where the value of this product is directly proportional to the value of PΔV
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