Explanation: This section prepares us for energy balances, much as we did for material balances. If you recall, material balances where not performed until chapter four. Before we could jump into doing material balances, we covered topics on units, pressure, temperature, and flow rates, to name a few. We were not prepared to solve material balance problems until we understood a few basic concepts and definitions. Similarly, this section introduces terminology, fundamental definitions and mathematical relationships required to perfom energy balances. |
Explanation: There are really three types of energy that we'll deal with often in chemical engineering: Kinetic Energy, Ek, Potential Energy, Ep, and Internal Energy, U. Closely related to Internal Energy is Enthalpy, H. Now, lets introduce the definitions, mathematical descriptions, and the concepts for each type of energy. Kinetic Energy Potential Energy
Internal Energy
Here, there are two equations to find the specific internal energy using a term with a hat over it (U-hat); the third equation is used if the heat capacity is a function of temperature (often for gases). The last equation is for a constant heat capacity, (often used for liquids and solids). Each of these equations involves the use of specific properties (those with hats over them, meaning that they are "per mol" or "per mass". Once we find the specific internal energy change with the third or fourth equations, we can find the internal energy change by multiplying it by the amount of substance undergoing that change. Additionally, we can find the rate of internal energy change (DU-dot) by multiplying by the mass or molar flow rate. It is assumed that U-hat has units of Energy/mass in the above equations, when the first formulas could be used. If U-hat has units of Energy/mole, of course, we would multiply the specific internal energy by moles (and not mass) to get the internal energy (using, for example, U = n * U-hat). It may be more correct to write U = (n or m) * U-hat. The key to getting this write is to pay attention to the units of the specific property. This of course applies to all specific properties (U-hat, H-hat, V-hat, etc.) and is probably a point that you are already familiar with. Enthalpy
Here, the usage of the first -> fourth equations is analogous to scenarios for those equations for internal energy already explained above. However, the last equations describe the relationship between enthalpy and internal energy. Similar discussions given above in the internal energy section about flow rates and specific properties are applicable here. |
Explanation: There are two types of energy transfer, heat and work. There should be a clear distinction between these two types of energy transfer and the forms of energy just mentioned. Where kinetic, potential, and internal energy are all forms of energy, heat and work are energy vehicles that move energy from one place to another. They act to transport energy by carrying energy from the surroundings into the system or from the system to the surroundings. Further examples follow, but let me give you one now: First, we need to name the system and the surrounding. The system could be a pot of water, and let's say that it experiences an increase in temperature (an increase in internal energy). The system gets energy from the surroundings and we say that this energy is transported by heat. Heat where the first notation designates some quantity of heat transported, and the second tells how fast heat is being transported per time. Work where the first expression designates the general work expression (units, Joule), the second designates work per time (units, Joule/second), and the third is the modified work expression that we will use for open systems, where the s subscript designates shaft work, such as work by a propeller (units, Joule/second). |
Explanation: "Energy is neither created nor destroyed." There are several other ways to say this, such as the energy of the universe is constant, or that energy doesn't appear spontaneously. That is, our cup of water doesn't increase its temperature sponaneously, but due to energy brought in from the surroundings via heat or work. This statement is what allows us to make the energy balances. Energy, like mass, is conserved. |
The last topic has to do with the way properties are given. In earlier sections, we determined that m stood for mass, and mdot stood for mass flow rate. Here, we can determine that V stands for volume, or Vhat, stands for specific volume, volume per amount (mass or mole). The following discussion leads to ways of differentiating between quantities such as volume and specific volume. First we introduce the two following definitions. Intensive properties: properties independent of the amount of material. Extensive properties: properties dependent on the amount of material. Explanation: Let me offer you a way to determine whether a property is an external or internal property - If the answer to the following question is yes, then the property is external (otherwise, it is an internal property): Does the property change if we go from one gram to a 100 grams for the substance? for example, determine whether the following properties are external or internal. mass (kg), temperature (K), volume (gallons), energy (joules), density (g/mL). The extensive properties listed here (those that change when we change the amount of substance) are: mass, volume, and energy. Now we understand how to categorize a certain property as extensive or intensive. Finally, note that any extensive property can be turned into an intensive property if it is divided by an amount. The resulting intensive property is called a specific property. For example, mass is an extensive property. If we divide mass by moles, we get an intensive property, namely, the molecular weight of a substance. We can divide an extensive property by either mass or an amount (such as moles) to turn it into an intensive property. The reason intensive and extensive properties are covered is to introduce specific properties because we will use them so much in energy balances. That is, many of the physical properties taken from the tables in energy balance problems are listed as specific properties. |
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