On the exam, you should be able to find thermodynamic properties very easily through the use of your thermodynamic property tables for given fluids, located in your Mechanical Engineering Reference Manual or Schaum’s Thermodynamics for Engineers. These properties are the building blocks for solving the problems on the exam. You should also have a concept of what these properties mean in the real world. These concepts will help to reality check your answers, instead of blindly following the results of your equations. Hopefully, this helps you to catch any math errors and speeds up your elimination of incorrect multiple choice answers.

Pressure

Pressure is one of the two most likely properties that you will start off with in a real world situation, because pressure is a thermodynamic property that is easily measured.

The pressure of a fluid indicates the amount of force per unit area that the fluid imparts on the materials around it. Pressure is typically measured in units of pounds per square inch (psi= lbf/(square inch)) . There are two different types of pressure scales, (1) absolute pressure and (2) gauge pressure. These two pressure scales differ by their 0 reference point. Gauge pressures have a 0-reference point as 1 atm. Thus 0 psig, where the “g” indicates gauge pressure, is equal to 1 atmospheric or 14.7 psia, where the “a” indicates absolute pressure. Most real world applications encountered by practicing engineers will have pressures indicated in gauge pressure. These include pressures measured at the discharge and intake of pumps and fans and the pressures measured at other pieces of equipment like heat exchangers, chillers and cooling towers. The relationship between gauge and atmospheric pressure is shown with the following equation and figure.

The relationship between gauge and absolute pressures, gauge pressure on the left and absolute pressure is shown on the right. See technical study guide for continuation.

Temperature

Temperature is the second property that you will start off with in a real world situation, because temperature is easy to measure.

This property is the one most people are familiar with, because it is displayed on thermostats and thermometers. Temperature is a direct indication of the amount of heat in the fluid. The United States Customary Systems (USCS) units used for temperature are Fahrenheit and Rankine. Typical Fahrenheit temperatures for chilled water (medium used for water-cooled air conditioning) range from 45 F to 55 F and hot water temperatures range from 120 F to 140 F. The temperature at which water boils is 212 F and water freezes at 32 F.

Rankine temperatures are used when it is necessary to define an absolute temperature scale having only positive values. The conversion between Fahrenheit and Rankine is shown below. When using equations during the exam, ensure that the correct temperature units are used. Always double check the required units for your equation.

Enthalpy

Enthalpy describes the amount of energy in a system. This property is used extensively in the Energy/Power applications. It defines the entering and leaving energy of a fluid through a system. On the exam, enthalpy refers to total enthalpy. Total enthalpy is equal to the internal energy of the fluid plus the energy due to pressure-volume.

See technical study guide for a continued discussion on Enthalpy.

Entropy

See technical study guide for the section on entropy.

Specific Heat

See technical study guide for the section on Specific Heat.

Thermodynamic Cycles

There are two main thermodynamic cycles that are a critical part of the PE exam and play an important role in the Thermodynamics & Fluids field of practice. These two cycles are the Brayton and the Rankine cycles. If you can understand these two cycles completely, then you should put yourself in a good position to pass the PE exam. This section will describe the principles that govern these cycles and will also introduce the diagrams that are used in these cycles.

Pressure-Enthalpy Diagrams

The pressure-enthalpy (P-H) diagram describes the liquid, vapor and mix region of a fluid and in this case water. As shown in the following figure, the P-H diagram consists of pressure (psia) on the y-axis and enthalpy (Btu/lbm) on the x-axis. It is important to note that pressure is shown on a logarithmic scale while enthalpy is shown in a normal scale. In the middle of the diagram is the vapor dome. This dome separates the sub-cooled liquid (aka water) on the left side, super-heated vapor (aka steam) on the right side and the liquid-vapor mix region (aka mixed region or wet region) in the middle.

The mixed region is cut by upward sloping lines that represent the percentage of vapor, as shown in the following figure. The figure shows that as you move from left to right on a constant pressure line, the percentage of vapor increases from 0% at the saturated liquid to 100% at the saturated vapor line. The percentage of vapor is also known in other terms as steam quality and dryness fraction, where saturated vapor has a steam quality or dryness fraction of 1.

See technical study guide for continuation on Pressure-Enthalpy diagrams.

Thermodynamic Tables

There are three main types of thermodynamic tables that the engineer must be able to use the, (1) Saturation Tables as a function of pressure; (2) Saturation Tables as a function of temperature and (3) Superheated Tables. From this point on, Steam shall be used as an example of a Thermodynamic table. But water/steam can be substituted for other liquids and the skills you learn here can be applied to other liquids.

Graphically the steam tables show the values of the outer dome on the pressure-enthalpy diagram. The following figure shows the points that are selected for the steam tables. This figure shows the values as a function of pressure.

See technical study guide for a continued discussion on Thermodynamic Tables.

Enthalpy-Entropy Diagrams

Enthalpy-entropy diagram shows graphically the various properties of fluids ranging from superheated region to the mixed region. The diagram does not provide water (liquid) properties. The following diagram and discussion shall focus on water/steam. A sample of the diagram is shown below in order to illustrate the main points of the diagram and how to use the diagram. The aspiring professional engineer should refer to the actual tables located in the Schaum’s Thermodynamics for Engineers or the Mechanical Engineering Reference Manual.

First, inspect the axes, note that the y-axis indicates enthalpy and the x-axis indicates entropy. The Mollier diagram shows only two regions, the mixed region of vapor and liquid and the super-heated vapor steam region. The two regions are separated by the downward sloping saturation line, where steam quality is equal to 1. Secondly, notice the upward sloping (left to right) constant pressure lines. Constant dryness fraction or steam quality lines are shown as downward sloping in the mix region. Finally, the diagram has slightly downward sloping constant temperature lines, which is only applicable in the super heat region.

Finding Thermodynamic Properties

One of the main skills that the aspiring professional engineer must acquire is the ability to determine the thermodynamic properties of fluids and in this case steam. In practice, the pressure and temperature of steam can be measured via pressure gauges and temperature gauges. However, the other useful properties of steam like entropy, enthalpy and specific volume must be found through the use of the (1) P-H Diagram, (2) Enthalpy-Entropy Diagram and (3) Thermodynamic Properties Tables.

A simple way to find the properties of steam given the temperature and pressure is to draw a simple P-H diagram. For example, assume water is at 14.7 psia and 60 F. Next draw a simple P-H diagram. It is known that at 14.7 PSIA (1 ATM), the boiling point is 212 F, thus the constant temperature line in blue can be drawn. Since the temperature of the water is 60 F, then the point must be located to the left along the horizontal constant pressure line. Note that since constant temperature lines are vertical in the sub-cooled liquid region, that the enthalpy of water at 14.7 PSIA, 60 F is equal to the enthalpy of saturated liquid water at 60 F. Take vertical line down from 14.7 PSIA, 60 F to the intersection of the saturated liquid curve.

See technical study guide for more information on how to find thermodynamic properties.

Thermodynamic Transitions

Thermodynamic transitions describe various movements a fluid may take in a thermodynamic cycle. These are the individual steps that will make a complete thermodynamic cycle. For example, a thermodynamic transition may be a fluid compressed from pressure state 1 to pressure state 2 or a fluid expanded from pressure state 3 to pressure state 4. The way the fluid moves from one state to the next will also provide more information on the thermodynamic properties of the fluid. For example, one of these transitions may occur isentropically (no change in entropy) or isothermally (no change in temperature). As an engineer you should understand each of these transitions and what equations can be used to find thermodynamic properties of fluids as the fluids go through the thermodynamic cycles.

• Isentropic Transition from Pressure State 1 to 2:
• Isobaric Transition with Heat Gain or Heat Rejection:
• Adiabatic: No change in energy
• Isothermal: No change in temperature
• Icochoric: No change in volume

See technical study guide for more detail on the above transitions.

Ideal Open Gas Turbine Cycle

The two major application areas of the open gas turbine cycle are for aircrafts and electric power generation. In an open cycle the working fluid (air) only passes through the cycle once and is then exhausted to the atmosphere. In a closed cycle, the working fluid (air) is recycled through the cycle. One assumption that you should be aware of is that the mass flow rate through both the open and closed cycles are assumed to be constant. Although fuel does enter the cycle, it is assumed that the only mass flow rate to be considered in doing problems is the mass flow rate of the air. This is typically a safe assumption because the ratio of air to fuel is quite large, typically fuel can be around 2% of the total mass flow rate.

The above figure shows the components of an open Brayton cycle. Step 1 to 2 is the isentropic compressor. Step 2 to 3 is a constant pressure combustion chamber. Step 3 to 4 is the isentropic turbine.

These figures show the constant entropy and constant pressure paths in the Brayton cycle. Use these figures with the previous figure to match each point to each piece of equipment. See technical study guide for more detail on the Ideal Brayton Cycle.

Ideal Brayton Cycle - Closed Gas Turbine Cycle

The Brayton cycle or closed gas turbine cycle is similar to the open gas turbine cycle, except the air is not exhausted to the atmosphere. In order to accomplish this, heat exchangers are placed at the combustion chamber section and at the exhaust section.

The above figure shows the components of a Brayton cycle. Step 1 to 2 is the isentropic compressor. Step 2 to 3 is a constant pressure heat exchanger. Step 3 to 4 is the isentropic turbine and Step 4 to 1 is a constant pressure heat exchanger.

This figures show the constant entropy and constant pressure paths in the Brayton cycle. Use this figure with the previous figure to match each point to each piece of equipment.

See technical study guide for more detail on the Ideal Brayton Cycle.

Actual Brayton Cycle - Closed Gas Turbine Cycle

The actual Brayton cycle is a little different from the ideal Brayton cycle, because processes do not occur isentropically in reality, meaning that entropy is added. Also excess heat or less heat can be added during the steps.
See technical study guide for more detail on the Actual Brayton Cycle.

Rankine Cycle

Steam power plants run vapor power cycles with water as the working fluid. This section introduces the ideal cycle for vapor power cycle, the Rankine cycle. These steam powered plants generate electrical power by taking the heat from combusting coal, oil, biofuel or natural gas. The power plant consists of multiple systems working together. An overall view of all systems together is shown below.

The thermodynamic cycle described by the yellow lines is called the Rankine cycle. This system consists of a boiler, turbine, condenser and a pump. Fuel, burned in the boiler, heats the water to generate superheated steam. The Rankine system is discussed in this section.

See technical study guide for more detail on the Rankine Cycle.

Energy Balances

A key concept in Thermodynamics is that energy is not created or destroyed in a closed system. This is called the first law of Thermodynamics. This concept is used in the cycles and in the cooling/heating questions. Energy balances are conducted around a piece of equipment and around a fluid or multiple fluids. The following are examples of the key equations that govern the energy balance across certain pieces of equipment. These energy balances are discussed further in other sections.

Turbines, Pumps and Compressors

Turbines, pumps and compressors change the amount of energy of the incoming fluid by changing the flow rate and pressure of the fluid. Pumps and compressors increase the flow rate and/or pressure of the fluid, while turbines reduce the flow rate and decrease the pressure of the fluid. In a pump and compressor, energy is transferred from a power source to the fluid. In a turbine, energy is transferred from a fluid to provide a power source. In both cases, this power source is called Work. Essentially work is transferred to or from these pieces of equipment.

Boilers, Condensers and Evaporators

Boilers, condensers and evaporators are pieces of equipment where a phase change in a fluid occurs. In boilers and evaporators, liquid is changed to gas and in condensers, gas is changed to liquid. In boilers and evaporators, energy is added into the system by the boiler or evaporator in order to heat the liquid to gas. In condensers, heat is removed from the system by the condenser in order to change the gas to a liquid. The energy balance equations governing these pieces of equipment take into account the phase change of the fluids.

Nozzles and Diffusers

Nozzles and diffusers are used to change the velocity of a fluid through the use of a change in pressure. So the fluid’s velocity and pressure will be different but the energy entering the nozzle or diffuser and leaving the nozzle or diffuser will be the same. This is assuming that there is no elevation change, no heat loss, no friction loss and no work done by the fluid.

Heat Exchangers

Heat exchangers are used to transfer heat from one fluid the other. Heat exchangers can be used to transfer heat from one hot liquid to a cold liquid, a hot air stream to a cold air stream, from air to liquid or from liquid to air. Since there is no phase change, the energy balance equation is only based on the mass flow rate of both fluids, the temperatures of these fluids and the heat capacity of both fluids.

Mixing

In feedwater heaters or in tanks, two fluids may be mixed together. The energy balance on these types of systems involves calculating the total energy of the fluids entering the system, which will equal the energy of the mixed fluid. A few equations shown below highlight this relationship. This mixing energy balance can be applied to both air and liquid. Similarly to boilers, condensers and evaporators, if a phase change occurs, then the energy change due to the phase change must be taken into account.

Combustion

Most power plants are driven by a chemical reaction called combustion, which usually involves fuel sources that are compounds of hydrogen and carbon and an oxidizer (air). Combustion is the process by which the fuel is oxidized and as a result releases heat. The process also releases water and carbon dioxide.

The equation for combustion is as follows:

When you substitute the basic formula for a hydrocarbon fuel and air, then the resulting equation is as follows.

See technical study guide for more detail on combustion including fuel, air to fuel ratio, stoichometry and excess air.

Steam

Steam is the driving force in power plants across the United States. You should be very knowledgeable about steam and especially how to read steam tables and find the properties of steam at various conditions very quickly.

Steam Tables

There are three main types of steam tables that the engineer must be able to use the, (1) Saturation Tables as a function of pressure; (2) Saturation Tables as a function of temperature and (3) Superheated Steam Tables. Graphically the steam tables show the values of the outer dome on the pressure-enthalpy diagram. The following figure shows the points that are selected for the steam tables. This figure shows the values as a function of pressure.

See technical study guide for more detail on steam, including pressure-enthalpy diagrams, steam tables continued, Mollier diagram and how to determine properties of steam given a set of initial conditions.

Vapor Compression Cycle

The vapor compression cycle is the primary cycle used in commercial refrigeration systems.

The vapor compression cycle starts at (Step 1) the evaporator, with cold, low-pressure, liquid refrigerant. It absorbs heat and evaporates to a low-pressure gas. Then the gas is (Step 2) Compressed to a high-pressure, high-temperature gas and (Step 3) condensed to a high pressure, low temperature liquid. Finally, the gas is expanded (reduced in pressure) at the (Step 4) expansion device to a cold, low-pressure liquid refrigerant.

See technical study guide for more detail on the vapor compression cycle including detailed information on each step, evaporator, compressor, condenser and expansion valve. In addition a second explanation is provided in terms of the P-H diagram.