Change in T or P

**ΔH = Q**, it's derivation and why it is so prevenlent from here on.- Finding ΔH for changes in pressure and temperature
- By using C
_{p}- By using tabulated enthalpy tables

- The relationship between ΔH and ΔU, and between C
_{v}and C_{p}

So far, we've covered many Energy balance topics. Where are we? Thus far, we have covered four energy topics. First, we covered some basic energy definitions (E For many of the rest of the problems in this class, ΔH = Q. Uh, what? I, myself am a global learner. In 201 and in thermodynamic courses (like ChEE 316 at Arizona), this expression is first derived from an energy balance before it is used extensively in the course material after where it's connection with energy balances fades. That is, we have learned a few energy balance expressions thus far, and for the most part, we will only apply this one reduced expression for the energy balances that will come in later classes. , resulting in a strong connection between the energy topics of the course.I would like to solidify the connection between chapter 7 and this equationIf you have just said to yourself, this is obvious, the link is clear. Chemical engineering processes usually involve flows, resulting in the use of the open energy balance. And, these processes don't usually involve valves (or other components that change the velocity -> changes in kinetic energy), or pipes involving great height changes (no potential energy), and there is often no stirrer (no shaft work). Hence, the connection between the expressions learned in chapter 7 and the ΔH = Q expression that will usually be used from here on out, is obvious. If this was you response then bravo, and you probably skip on to the interrelations of this section, if your response was "hmm", or "huh?", then take a moment, and read on to solidify the connection. Make the connection
Keeping in mind the basic equations we learned in chapter 7, and the energy balance equations for closed, open, and mechanical systems, let's consider a simple chemical process where methanol and water are separated in a condenser. What energy equations would you apply to the following system? How? So, consider your energy balance tool box: Which tool do you use, and how? Well, in the tool box we have a closed energy balance, an open one, and a mechanical system energy balance equation. There are streams in this problem (flowrates), thus the system is not closed. There are no valves or huge height changes so the system is not a strictly mechanical system using only a mechanical energy balance. Thus, it is clearly Finally, the equation is:an open system where only the open energy balance equation applies. ΔH+ΔE ΔH+ ΔH=Q |

Now we understand the infamous expression ΔH = Q, where it comes from and why it recurs often in chemical engineering. Next, we will learn how to find ΔH (and thus Q) for various scenarios. On this webpage we will learn how to do this for changes in temperature and pressure. A later webpage will show us how to do this for changes in state and for chemical reactions. ΔH for a Here, the following expression is used to calculate the change in enthalpy for solids, liquids, or ideal gases. ΔH = H_{final} - H_{initial}_{initial}
where,H _{final} and H_{initial} for several different compounds are found directly from tables (such as table B8, B9), or for water from steam tables (such as tables B6 and B7). For the specific system of air and water vapor, the text offers a psychrometric plot (a cross-plot that relates several properties on on one plot) we can use to get H_{initial} and H_{final}.
For a tutorial on how to read a water vapor - air psychrometric chart, click here.In our problem solving, we would opt to find the enthalpy change for a change in temperature by consulting one of the tables or charts. ΔH for a Here, the interrelations to calculate enthalpy change are very straight- forward: ΔH for a All we do for a system in which there is a pressure change and a temperature change is simply calculate the ΔH for the temperature change, and then ΔH for the pressure change. Then we add up the two pieces to get the total ΔH. We can do this because enthalpy is a state function and we can use any pathway to add terms up in order to find the total. _{change in T & P} = Δ H_{from T1 to T2} + ΔH_{from P1 to P2}Where the relations for ΔH _{from T1 to T2} and ΔH_{from P1 to P2} for solids, liquids, and gases have been given above.
The interrelations given here are not very complex. However, there are many different ways that we can choose to use when solving for these terms. The most important aspect of using them is clearly not math, it is reading the problem statement and recognizing that you have a temperature or pressure change between the inlet and outlet streams, and that you need to find ΔH. Then you need to be able to quickly choose a good method where you can find all the data you need. In the next section, the definitions of ΔU and C |

This should serve as Relating ΔH to ΔU:This applies to solids, liquids, and ideal gases.
_{p} = C_{v} + R (for ideal gases)where R is the ideal gas constant. Getting ΔU from C_{v}This interrelationship applies for a temperature change (at constant volume), and is analogous to the expression relating ΔH and C _{p}._{V}(T) dT, T_{1} TO T_{2}The relationships and equations were given here in this section so you can see how the variables are interrelated and can be interchanged. Also, remember that the open energy balance is used for a reason (flowing streams). Most of the systems in chemical engineering are open ones so an emphasis was placed on expressions of ΔH first. |

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