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Module 4: Liquid Characteristics - Enthalpy
Introduction
Enthalpy of Vaporization
Sensible Energy of a Liquid
Sensible Energy of a Gas
Practice Problems
Objective
- Determine the amount of water necessary to cool a gas stream to a desired temperature by calculating the change in enthalpy.
Enthalpy (designated as H) is an important property in thermodynamics
and is regularly used in air pollution control. Enthalpy represents the
total useful energy in a substance. This useful energy is measured in
terms of internal energy, which is a type of energy that occurs at the
molecular level. Change in enthalpy 
is a more useful concept than the concept of enthalpy by itself. The change
in enthalpy represents the amount of energy removed from or added to a
substance (e.g. water or air) as it changes temperature, including the
energy released from or added to the substance as it undergoes a phase
change (i.e. solid, liquid, and gas).
In air pollution control systems, it is often necessary to cool a gas stream before it enters a control device to prevent damage to the equipment. For example the fabric of bags in fabric filters can be damaged at certain temperatures. Cooling the gas stream may also be required for the control device to work efficiently, as is the case for electrostatic precipitators (ESPs). Change in enthalpy calculations can be used to determine the amount of water necessary to cool a gas stream to the desired temperature. In the process of cooling the gas stream, the temperature of the water increases while the temperature of the gas decreases to the desired temperature.
This lesson focuses on the change in enthalpy of liquids as they change temperature. For more information about the enthalpy of gases, refer to the Heat Capacity and Enthalpy lesson in Module 2.
Enthalpy is often recorded as energy per unit mass as shown in Table 1.
Equation 1 is the general equation for determining the change in enthalpy
of a liquid as its temperature increases from T1 to T2 and the liquid
undergoes a phase change (i.e. evaporation).
- Where:
Equation 1 can be rewritten as follows because the sensible energy of a liquid, the enthalpy of vaporization, and the sensible energy of a gas are represented as a change in enthalpy.
Sensible energy is the measure of the change in internal energy experienced by a substance during a change of temperature that does not involve a phase change (e.g. evaporation). The sensible energy of a liquid corresponds to the amount of energy required to raise the temperature of substance in the liquid phase from one temperature to another. In this example, the temperature of the liquid is rising from temperature T1 to its boiling point (BP). At the boiling point, an amount of energy corresponding to the enthalpy of vaporization for the substance represents the phase change from liquid to gas. The sensible energy of the gas represents the energy required to increase the temperature of a substance in the gas phase from one temperature to another. In this example, the temperature is rising from the boiling point (BP) to temperature T2.
The phase diagram below illustrates this concept graphically. Changes in the sensible energy of a substance are reflected as a change in temperature. During a phase change such as evaporation, the substance undergoes a change in its enthalpy without experiencing a change in temperature.
Note: Sensible energy and enthalpy of vaporization are sometimes referred to as sensible heat and latent heat of vaporization, respectively. The field of thermodynamics no longer uses the term "heat" in this context because it is a misnomer. Heat is only one form of energy that can be transferred during changes in internal energy and enthalpy.
When the temperature of the liquid reaches the boiling point, the vapor pressure equals the pressure of the gas stream. At this temperature, vaporization occurs not just at the gas-liquid surface, but throughout the liquid. Bubbles can form inside the liquid since the vapor pressure is sufficient to push back the gas stream surrounding the liquid. This is the reason that bubbles begin to form on the bottom of a pan of water that is being heated. Boiling will continue as long as energy is being supplied and there is liquid remaining to vaporize. The temperature of the liquid remains constant during boiling since the energy being added is used to increase the kinetic energy of the molecules and overcome the attractive forces between the molecules.
The amount of energy required to evaporate a liquid at its boiling temperature is represented by the enthalpy of vaporization.
-
- #1
- The enthalpy of vaporization for five liquids is provided below.
Based on this information which liquid would be the most efficient in
cooling a hot gas stream?
The sensible energy of a liquid is the amount of energy transferred to (or from) the liquid as its temperature increases (or decreases). This section concentrates on the sensible energy of water since water is almost exclusively used as the liquid for air pollution control applications.
A Btu is the amount of energy that must be transferred to one pound mass of water at 68°F to increase its temperature by 1°F. While a Btu is defined with respect to water at 68°F, the amount of energy that must be transferred to raise the temperature of a pound mass of water by 1°F, at any temperature where water is in a liquid form, does not vary significantly from one Btu. In fact this number does not vary by more than 1%. Therefore, the sensible energy of liquid water can be defined by Equation 3.
- Where:
Note: T1 and T2 in Equation 2 must be between 32°F and 212°F.
For liquids other than water, replace the specific heat value for water (1 Btu/lbm°F) in Equation 3 with the specific heat value for that particular liquid. Specific heat values are provided in most textbooks on thermodynamics.
The sensible energy of a gas is the change in internal energy as the gas heats (or cools) from one temperature to another.
- Where:
Table 3 provides the enthalpies of five gases at different temperatures and can be used to calculate the sensible energy of these gases.
Example Problem 1.
Calculating the Change in Enthalpy of Water
Calculate the change in enthalpy
per pound mass of water as it is heated from 60°F to boiling, as
it boils, and as the water vapor is heated to 400°F.
Solution:
Basis: 1 lbm water
- Calculate the sensible energy as the temperature of the water rises
from 60°F to 212°F.
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- From Table 2, the enthalpy of vaporization
of water is 970.3 Btu/lbm.
- Calculate the sensible energy as the temperature of the water rises
from 212°F to 400°F.
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From Table 3, H of H2O(400°F) = 131.3 Btu/lbm.
Interpolate data from Table 3 to obtain the value for enthalpy of water at 212°F. For the general interpolation formula see Module 2, lesson on Heat Capacity and Enthalpy.
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- Calculate the total change in enthalpy per pound of water.
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Example Problem 2.
Gas Stream Cooling Requirements
Calculate the amount of water at 60°F that must be sprayed into
the 20,000 ACFM hot gas stream prior to entering the electrostatic
precipitator (ESP). (See Figure 2). 
Use an inlet gas temperature of 2000°F and an inlet pressure of -10
in. W.C. Use a maximum inlet gas temperature to the precipitator of 400°F.
Assume that the inlet gas stream has a composition that is essentially
identical to air.
Solution:
Step 1. Calculate the inlet gas flow rate (lbm/min).
- Convert the gas flow rate from ACFM to SCFM.
(1).gif)
- Calculate the inlet gas flow rate (lbm/min). The average
molecular weight of air is 29 lbm/lb mole.
(2).gif)
Step 2. Calculate the change in enthalpy
of the air as it is cooled from 2000°F to 400°F on a Btu/min
basis. (See Table 3).
Note: Refer back to Module 2, lesson on Heat Capacity and Enthalpy as necessary.
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Step 3. Calculate the change in enthalpy
per pound of water as it is heated from 60°F to boiling, as it boils,
and as the water vapor is heated to 400°F. The answer is provided
in Example Problem 1.
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Step 4. Calculate total quantity of water required in gal/min (gpm).
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Reminder: Consult "Conversion Factors" under the "Quick Reference" button for information about converting between pounds and gallons.
Practice Problems
Enthalpy
- Instructions:
- Complete the Practice Problems before proceeding to the next lesson. Click on the button below.