 In this lecture, what we will do is we will take a look at different forms of heat transfer that could be involved within the first law of thermodynamics, we'll also take a look at different forms of work, we'll take a closer look at the definitions of internal energy as well as enthalpy, and finally we'll take a look at the first law for an open system. So beginning what we'll do we'll take a look at the different forms of heat transfer that could be involved within any of the problems that we look at with mechanical engineering thermodynamics. So there are three main forms of heat transfer. If you've taken a course in heat transfer these are the ones that you would have studied. Heat can be transferred via conduction, and that's where you have heat transfer going through a solid, and the heat transfer itself is being driven by a temperature gradient within that solid. And so the way that we express this is using Fourier's law, K being the thermal conductivity of heat, A being the cross-sectional area with which the heat is flowing through, and then there needs to be a temperature gradient, and so this would be for one-dimensional conduction that we'd be looking at, and with that you can calculate the heat transfer rate. A second form of heat transfer commonly found is involving a interface between a solid boundary and a fluid, and that would then become what we call convective heat transfer or convection. And this usually involves a fluid flowing and carrying the thermal energy within the fluid itself from the boundary. And the way that we express this is with the equation HATS, which TS is the surface temperature of the object where heat is either going into or being removed from, and T infinity is the free stream temperature of the fluid flowing past the object. And so here H is the convective heat transfer coefficient for that particular case that you'd be looking at. So it would depend upon the Reynolds number of the flow or the Grashof number of its natural convection. So that is the equation for convection. And finally there is another form of heat transfer that is a little different from the first two, and that is radiative or radiation heat transfer. And the reason why it's different is because you do not need to have physical contact between one surface and another in order to have this form of heat transfer. And the way that it is expressed, we have an emissivity coefficient, the Stefan-Boltzmann constant, the area, and then we have the surface temperature of the object expressed at a power of 4. And here the temperature is in Kelvin. So you have to be careful. The other ones could be in degrees Celsius or a degree Kelvin or degree Fahrenheit, degree rank, and depending on which unit system you're using. But for this equation it's very important that you use degree Kelvin or Kelvin. And it is then the difference between the surface temperature and the surrounding, and raised to the power 4 for both of those. So those are the three forms of heat transfer that we can encounter. And in thermodynamics we tend not to dive into details about the heat transfer mechanism itself. Usually this is just a value that is provided. It would be within a heat transfer course where you would go into details and study these different forms of heat transfer. So those are the forms of heat transfer. The next thing we want to take a look at are the forms of work. Recall in the first law we have heat transfer and work. So there are different forms of work that can appear in the equation. We can have work crossing the boundary of whatever, either if we have a fixed mass system. So the one that we talked about earlier with the closed system, or we can have an open system where you have mass flowing across the boundaries. But if you have work it will be going across the boundary itself, just like heat transfer as well. But we have electrical. So you could have a wire coming into your control volume. And you could have an electric resistance heater within your control volume. And so that would be generating heat and then the wire would leave again. So current is flowing through there. And there is a voltage difference. But that is doing work. So that's one form of work. And we express that as work is equal to the voltage times the current flow times the time. Because voltage is typically expressed in terms of joules per coulomb. Current is in terms of coulombs per second. And that thing gives you joules per second. And you multiply that by the delta t and that would then give you something in joules or kilojoules. Another form of work that we have is boundary work. And work at the boundary is going to be expressed as being the pressure at which the boundary is moving into multiplied by the change in volume. And we integrate this because the pressure could change as a function of change in the volume. So that is referred to as being boundary work. We also have gravitational work. And work attributed to gravity. That would be moving through a potential field. In this case it is that of gravity. And you have to be going through some sort of differential in position. And that is expressed as z2 minus z1. So that would be equal to a change in potential energy. Acceleration. When we change the velocity of the system we are doing work. And that work is expressed as the change in kinetic energy of the system. So you could have this as being one half times the mass times the velocity at state 2 squared minus the velocity at state 1 squared. And that would be equal to the change in kinetic energy of your system. Shaft work. This is when you have a shaft going across your control boundary. And there is a rotating shaft at a given torque that requires the rotations. So for example if we have an impeller within our control system or control boundary that we're looking at. And that propeller is churning the fluid and creating heat. Well that can be attributed to shaft work. And we talked about that in an earlier lecture. And the way to quantify that work is basically the number of revolutions multiplied by the torque being exerted on the shaft. So here n is equal to the number of revolutions. And tau is equal to the torque. And so with that you're doing work on the system. And you're quantifying that with shaft work. A final form of work that we'll talk about is spring work. And that would be where you're doing work by extending a spring. And so the work for that can be expressed in terms of the spring constant. And x2 and x1 would denote the final and the initial position of the spring. And note that it is squared in this equation. Now there are other forms of work that you could have. You could have work due to moving an object in a magnetic field. You could have work due to moving an object within an electrostatic field, for example. You could also have work due to surface tension if you're drawing a system and changing an interface between a liquid and a gas. You would have surface tension effects there. But these are some of the different forms of work that we'll be seeing in this course. Typically for the most of our problems what we're looking at will be acceleration, gravitational, boundary, and a little bit of shaft work. Once in a while you might have spring work. But those are the forms of work. Now let's take a look at the first law for a closed system. We talked about this in an earlier lecture. So if you recall we had q minus w is equal to the change in internal energy plus the change in kinetic energy plus the change in potential energy. Now what I'm going to do here is I'm going to take work and I'm going to say that it consists of what we'll call other work plus work boundary. So this would be a closed system where you may have the boundary of that system changing. For example a piston cylinder device where the piston is free to move up or down. You would have boundary work there. The forms of other work could be some of the ones that we just talked about in the previous slide. So if we break work into that form, boundary work plus other forms of work, and then introduce that into the first law, we get an equation that looks like this. Now what you'll notice that I've done is I've pulled the boundary work onto the right hand side of the equation. It was originally on the left and I pull it over onto the right hand side. And what we're going to do, we're going to lump these two values together, the internal energy and the boundary work. And we can write the first law for a closed system and it will look like this. So it's a different form of the first law from what we've seen before for a closed system. However, the main change is that we've introduced this term here, which is the enthalpy. And what enthalpy does is it takes into account the boundary work that you would have for your closed system. So on some problems that you may be examining, so let's say you have a piston cylinder device like this and you have mechanical stoppers here, and then you have your cylinder, sorry they're the piston, and if the piston is moving up, it is doing boundary work because it is encountering a pressure in order to move and change the volume. This is a fixed mass problem, but in order to account for that boundary work, what you can do is you can solve the problem using enthalpy instead of internal energy and it will account for the boundary work which is embedded within the system. So basically it's kind of a simplification of the first law for cases where you have a closed system but with a moving boundary.