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This is the third lesson in the series on psychrometrics. Lesson 1.3 provides a review of energy, enthalpy, sensible and latent heat, and their importance in psychrometrics. Please note this is intended to be a review only of basic fundamentals. Energy and enthalpy are complex topics. The purpose here is simply to give a brief overview.

Energy is a challenging and abstract concept to define. Energy has been described as the ability to do work. In building systems, energy consumption is a primary focus to architects, engineers, and of course, building owners. Energy exists in a number of different forms. A body can have potential energy, kinetic energy and chemical energy as some examples. Energy can also be transferred from one body to another. Energy transfer can occur in a number of different ways. This tutorial will limit the discussion to two forms of energy transfer that are of significance in building environmental systems. The first is work, and the second is heat transfer.

Work is the effect created by a force. For work to happen, the force has to result in a displacement of the body. Shown as an equation, work is equal to force times distance. The units for work are quite varied. In the SI, or metric, system, work is expressed in joules. A joule is the force of one newton through a distance of one meter. Also, the kilowatt hour is a unit for work. In the IP, or imperial, system, units used for work can be quite confusing. For instance, there is the foot-pound, the btu and even the horsepower-hour is an interesting unit for work.

**Example 1.3.1:**

This is an example on calculating work. A contractor has the job of installing an air conditioning unit on the top of a roof. The unit has a total weight of 10,000 lbs and needs to be hoisted up 30 feet. The question is: How much work is done in lifting the unit to the roof. To solve, we will use the equation for work which is work is equal to the force times the distance. Force, in this example, is the weight of the unit. The distance, of course, is going to be 30 feet.

The work, then, is 10,000 lbs times 30 feet. The work is 300,000 foot-pound. Power is also an important concept in building systems. Equipment capacity for chillers, boilers, pumps, fans and cooling towers is based on power. Although in each of these instances, the units to describe the power or capacity is very different. Simply stated, power is work per unit of time and written as the equation power= work divided by time. Please note that this is a highly simplified version of a very complex concept. But it is sufficient enough to illustrate the power in our discussion.

Just as with work, power has a number of units commonly used depending on the application. In the metric system, the basic unit for power is the watt and also the kilowatt. Please note the watt is based on the definition for power as the watt by definition is a joule per second. In the imperial system, there are a variety of units used for power. These include horsepower, foot-pounds per minute, where 33,000 foot-pound per minute is equal to 1 horsepower. Btu per hour, and this is sometimes written as Btuh, and ton of refrigeration.

**Example 1.3.2**

For the air conditioning unit, calculate the minimum power required if it takes 5 minutes for the unit to reach the roof. Give the answer in units of ft-lb/min, hp and kW.

The solution here is to see the equation for power, where the work is 300,000 ft-lb and the time is 5 min. Then the minimum power would be 300,000 ft-lb divided by 5 minutes, or 60,000 ft-lb per min. A couple of useful conversion factors are: 1 Hp = 33,000 ft-lb per min and 1 Hp = .746 kW. We can convert this using unit analysis. 60,000 ft-lb per min times the conversion factor of 1 Hp per 33,000 ft-lb per min gives us 1.82 Hp. Then we can convert 1.82 Hp by multiplying .746 kW per Hp gives us 1.34 kW.

As noted earlier, energy can be transferred from one body to another. Work is a form of energy transfer. Another form is heat transfer. For purposes of this tutorial, I’ll use Q to designate heat transfer. In building environmental systems, heat transfer is very often calculated in units of Btu which stands for British Thermal Unit. One Btu is the amount of heat required to raise the temperature of 1 pound of water by 1 degree fahrenheit.

Finally, this leads us to enthalpy. Enthalpy is of utmost importance in the study of psychrometrics. In this particular view of a standard psychrometric chart published by ASHRAE, lines of constant enthalpy are shown as diagonal lines from upper left to lower right. So, what is this property called enthalpy? Well, technically speaking enthalpy is a combination of a body’s internal energy plus the product of its pressure times volume. Enthalpy is a measure of the total energy of the system. You might hear the definition of enthalpy as the property of a body that measures its heat content. Scientifically speaking, this is not correct but it is used so often that for the purposes of discussing psychrometrics, we will accept this definition. The units for enthalpy in the IP system is the Btu. Specific enthalpy is Btu per lb. In the metric or SI system of units, the unit of measure for enthalpy is the Joule.

**Sensible and latent heat:**

When heat is added to an open container of water, at conditions such as for example an atmospheric pressure at sea level, a noticeable change occurs. Adding heat to the water results in a temperature increase. This is called sensible change. In sensible change, the temperature rises as the enthalpy of the container of water is increased. The increase in enthalpy is called sensible heat. At some point, adding additional heat does not show an observed increase in temperature as the liquid gradually changes into a vapor state. This change is referred to as vaporization, and for water, we call this boiling. Although the temperature does not change the enthalpy is still increasing. This is what is referred to as latent heat. The entire process of sensible change and latent change is the total change and the enthalpy change is the sum of the sensible heat plus the latent heat.

**Specific Heat:**

Specific heat of a substance is the amount of heat per unit of mass required to raise the temperature by one degree. In the Imperial System of units, specific heat is in units of Btu per lb per degree fahrenheit. Since psychrometrics is the study of moist air properties, it is helpful to understand the specific heat of the air and water. For water, the specific heat is 1 Btu per pound-degree Fahrenheit. The specific heat of air is .24 Btu per pound-degree Fahrenheit. Please note that this is about one quarter of the value for water. This difference in specific heat between water and air has significant impact on the design of HVAC systems since these systems often involve the removal or addition of heat from air or water. The sensible heat equation is used extensively in HVAC systems. The sensible heat equation quantitatively describes the heat that is added or removed from a substance during sensible change. It’s shown as equation Qs= Mass flow rate times the specific heat times the change in temperature. Shown another way, Qs= m x C x (T2-T1). The dot designates that it is a rate. Units are very important here. When shown to represent a rate, such as Btus per hour, the mass flow rate needs to be in pounds per hour, specific has to be in Btu per pound-degree fahrenheit, and the temperature change is in degrees Fahrenheit.

Using the sensible heat equation is very useful, but its limited to processes that involve a sensible change only. The heat added or removed in HVAC processes can also be determined by the enthalpy equation. This is important because it is very useful in understanding complex processes that involve both sensible and latent heat change, such as in dehumidification. Written as an equation, Q is equal to the mass flow rate times the change in enthalpy. To find Q in Btus per hour, the mass flow rate is in pounds per hour and the enthalpy is in Btu per pound.

The following example, example 1.3.3 illustrates how sensible heat equation can be used in determining airflow. A 5 kW electric resistance heater is installed in a duct. Measuring the temperature of the air before and after the heater shows the air temperature has an increase of 30 degrees fahrenheit. Use the sensible heat equation to determine the airflow rate in cubic feet per minute or CFM.

The first step in solving this problem is to convert the heater capacity from kW to Btu/hr. 5kW times the conversion factor of 3410 Btuh/kW results in 17,050 Btuh. Please note Btuh is the same as Btu per hour. You will see both of these used commonly in describing HVAC applications.

The next step is to apply the sensible heat equation. In step 1, the heat transfer from the heater to the air was found to be 17,050 Btuh. This is Q dot in the equation. Since the fluid is air, the specific heat shown here as C is the specific heat of air. We will use 0.24 Btu/lb-degree fahrenheit in this example. The temperature difference is the leaving temperature minus the entering temperature. And now, using some algebraic rearrangement we can solve for the mass flow rate of the air. Solved by entering the values and doing the math, the airflow rate is found to be 20,368 pounds per hour. But pounds per hour is not very practical in HVAC applications, so the final step is to use the average density for air and some unit analysis. So, 20,368 pounds per hour times 1 hour per 60 minutes times 1 cubic foot per 0.075 pound of air, which is the average density of air, will give us 526 cubic feet per minute, also known as CFM.