 This is the second exam from the spring 2015 semester of thermal one and it covered chapters three to four from the Moran and Shapiro textbook. It was generally about evaluating properties and then analyzing some open as well as closed systems. So 30% of the points came from multiple choice theory questions. I guess five multiple choice questions, one short answer question. The remaining 70% of the points came from three workout problems. So two workout problems were open systems. One workout problem was a closed system, but they all involved some amount of property determination. Anyway, let's jump into the multiple choice questions. Question number one. In this PV diagram, the quality at state beta is best represented by which the following. So this question and actually the first three questions are all referring to quality. Remember that quality is a property that is used to describe a saturated mixture and it represents the mass of the vapor, rather the ratio of the mass of the vapor in the mixture to the total mass of the mixture. So if you had a saturated liquid vapor mixture and 25% of it was vapor, 75% was liquid, then you would have a quality of 0.25. So this PV diagram is representing the saturated mixture region. Over here would be a liquid. Over here would be vapor and then underneath this dome is a mixture of liquid and vapor. So we call this region liquid, compressed liquid, because this left-hand side or this left-hand line of the dome represents saturated liquid. This right line of the dome represents saturated vapor. So if it's liquid when it's on this line, then compressing it more makes it a compressed liquid. If it's vapor on this line, then superheating it more makes it a superheated vapor. Then the mixture region is a combination of liquid and vapor. So if you started off with liquid water and you added heat, eventually it would reach a point where it could not contain any more energy without changing phase. It's saturated with energy. At that point the additional energy turns the liquid into vapor partially and while it's making that transition, it's moving across this dome. Once it reaches a point where it's all vapor, it can begin to heat up again, then it enters the superheated vapor region. So quality can be used to represent the proportion of the way across the dome that the mixture is because over here a hundred percent of the mixture would be liquid and right here a hundred percent of the mixture would be vapor. So beta here is going to be between the liquid and vapor. It's going to be somewhere in the middle. So over here, a saturated liquid, we would call this a quality of zero and over here at a saturated vapor, we call that a quality of one because at that point it's a hundred percent vapor. Over here it's zero percent vapor. Therefore beta is going to be somewhere between zero and one. So the answer to question one is C. Now question two in this PB diagram, the quality at stake gamma is best represented by which of the following. So gamma is over here and a pretty common error here would be to say well zero is over here, then we're increasing it for a while. Eventually we reach a point where quality is one, so if we continue to go to the right, that means that the quality must increase, right? Therefore quality is greater than one? No, because quality is a property that only makes sense when you're describing a saturated liquid vapor mixture. It doesn't have any meaning outside of this region. You know if I asked you what did you get for a grade on that last thermo test and you said A, that is a completely normal answer because that grade is used to describe performance on an exam. But if I asked you how did you do in that football game and you said A, that doesn't make any sense because you don't get ascribed a grade in a sports game. At least you generally don't, I'm assuming. I don't know how sports work. Whatever the case, the point is it's not a quality of greater than one. Here, quality has no meaning, therefore it's actually none of the above. Question number three. In the above PV diagram, the phase at state alpha is best represented by which the following. So alpha is right on the saturated liquid line, therefore it is a saturated liquid. Question number four. What could you say about the specific enthalpy at points alpha and beta? So this is referring to these two points on this PV diagram and I'm asking which enthalpy is greater or are they the same? And there are a couple of ways to answer this question. You could, for example, look at the definition of specific enthalpy. It's lowercase h is referring to specific enthalpy and we define that as being the specific internal energy plus the pressure times specific volume. So you could look at this and say, well, I know internal energy is increasing from alpha to beta so this quantity is going to be going up from alpha to beta. The pressure is going to be constant because alpha and beta are horizontal on this pressure specific volume diagram, therefore they have the same pressure and then beta has a higher specific volume, therefore the specific volume is also increasing. So if this quantity and this quantity is increasing, it must mean that the specific enthalpy at beta is greater than alpha. You could also have looked at this and said, well, I know that when I have water sitting in a pot on my stove and I want to bring it from a liquid to vapor stage, I want to make it boil, I have to add energy. If I'm adding energy to the water, I'm increasing its enthalpy, therefore the enthalpy at beta is greater than alpha. If you didn't know any of those relations, you could have always turned to your textbook. So if we flip to the textbook and I'm going to do something I don't normally do here, I'm going to refer to the table of contents. This is the appendix A, rather the appendix and SI units. So if I were to just pull out the properties of saturated liquid, that would be tables A2 and A3 and I want to look at a plot by temperature because I'm looking at a line of constant temperature. On this diagram, the dashed line represents a line of constant temperature. So alpha and beta are both on that line. They have the same temperature. They also have the same pressure. So I'm going to look at table A2, that's on page 927. Okay, so if I just picked out an arbitrary temperature here, I'm arbitrarily assigning this graph as being water and I'm arbitrarily assigning a temperature to this. If I just said, let's consider a temperature of 25 degrees Celsius. Well, the enthalpy of the saturated liquid, which is 25 degrees Celsius, would be 104.89 kilojoules per kilogram. So on this diagram, we could say that the specific enthalpy of alpha is hypothetically 104.89. Then I know that the quality is going to be increasing from alpha to beta, therefore beta is going to be somewhere between these two numbers, somewhere between the saturated liquid and the saturated vapor-specific enthalpies. And I can kind of eyeball this and say, well, the quality of beta is going to be about 0.75, so it's going to be closer to a vapor than it is to a liquid, therefore the enthalpy is about maybe 2,000. But regardless, no matter what the quality is, I know it's greater than zero, therefore the enthalpy is greater. And we can see here that as we move from left to right of the specific enthalpy here, that number is increasing. Therefore the specific enthalpy of beta is greater than alpha. Well, anyway. I'm getting kind of off the point there. Question number five. Which of these are common assumptions that we make about nozzles? Well, a nozzle, at least a subsonic nozzle, is a device whose purpose is to convert enthalpy into kinetic energy. So we have some inlet of our nozzle. Let's call this state one, maybe. And across the nozzle, it's going to be increasing in velocity. And since that energy is coming from the enthalpy, the pressure is going to be decreasing. So from one to two, I am increasing the velocity. That's not an equal sign. There we go. That's much more better. And I'm going to be decreasing the pressure. And when we're analyzing the nozzle, we generally assume that they are adiabatic. That's not necessarily because they are well insulated. It could just mean that this process is happening relatively quickly. The fluid isn't in the nozzle for very long, so it doesn't have much time to exchange heat. That could be what we're assuming. But regardless, we generally assume that they are perfectly insulated. So in our analysis, we're going to say that the change in kinetic energy is not equal to zero because that's what we're trying to accomplish. And I know that the change in enthalpy is not going to be zero because I'm getting energy from the enthalpy in order to increase the kinetic energy. Then I know that the heat transfer is going to be assumed to be about zero because it's assumed to be adiabatic. And then there are no sources for work to occur, at least no obvious sources, so we generally assume that the work is zero. So over here, we would be saying that the C and D are both correct. But what about potential energy? Well, if we go back to this diagram, I've shown one and two as being approximately equal to each other in height. Therefore, the potential energy is also relatively equal. But even if this were vertical, the distance between one and two would not yield a significant enough difference in the potential energy to really matter relative to the change in kinetic energy and enthalpy. So we generally assume that the potential energy is also zero. And lastly, we generally assume that the nozzle doesn't have any space to accumulate mass. We assume then that it operates the same no matter when you look at it. Assuming everything before it and after it is the same, none of the properties within the nozzle will change with time. So the inlet temperature, for example, might be different from the outlet temperature, but the inlet temperature itself will be constant. Any property will be constant with respect to time, meaning that we treat it as being steady state. Question number six. In one or two sentences, describe an example situation where it would be reasonable to assume that the specific heat capacity was constant and talk about what things specifically allowed you to conclude that the assumption was reasonable. The key points I was looking for were that the substance had a relatively small temperature change and that there was no change in phase. So we could say, well, maybe a kettle heating water to make tea. So let's say that the kettle was heating water to make green tea. So green tea is optimally brewed at 80 degrees Celsius. So if we assume that it started at room temperature, then going to a temperature of 80 degrees Celsius, that represents a relatively small temperature change and no phase change. And that's the multiple choice questions.