 So, we have discussed displacement work quite extensively so far, derived the expression for displacement work and also went through a few examples illustrating the application of integral PDV. Notice that the most important thing is to actually identify the system. When you before you apply integral PDV, you must identify the system, then apply integral PDV to that system, especially to those parts of the system that are undergoing deformation. So, the P is the pressure in that part of the system which is undergoing deformation and the DV is the change in volume in that part of the system which is undergoing deformation that is very, very important and that is the reason why we went through many examples in the beginning when we discussed the definition of system to demonstrate how to properly define a system. So, that is very, very important, defining the system is very, very important. So, that deals with displacement work. Now, there are also other forms of work. We will discuss a few of these which are of relevance to engineering thermodynamics. The next one is shaft work. So, when we apply a torque T to a shaft and it turns through an angle theta, then the work done is given by, work done is nothing but the torque T times the angular displacement. Now, if under the action of this applied torque, the shaft begins to rotate at a speed of say n revolutions per minute or 2 pi n radians per minute, then the work done is nothing but T times 2 pi n joules per minute or in other words, the shaft power is given as 2 pi n times torque divided by 60 watts. When we supply a shaft power for let us say T seconds to a device, then the work that we have supplied is equal to 2 pi n torque times the duration divided by 60 joules. So, we will be making use of these expressions in examples that we encounter later on. Electrical work, we saw how a battery supplied electrical work. So, when a current of I amps is supplied from a source across a potential difference of V volts for a duration of T seconds, then the electrical work done by the source is given as V times I times T. So, it is a product of the voltage times the current times the duration for which the current is supplied. Spring work, we have already seen this when a linear spring of stiffness K Newton per meter is compressed by an amount of X meter work done on the spring. Notice that this is work done on the spring is half K X square or work interaction for the spring is minus half K X square. So, these are the forms of work that we are likely to encounter in our course. There are many other forms of work and expressions for these are available in standard literature, but these are the forms of work that we are going to that we are likely to encounter. Another one or another form of work is the so called paddle or stirring work. This occurs in many applications in mechanical engineering as well as chemical engineering where contents of a vessel have to be stirred to maintain a temperature or to maintain the composition homogeneous and so on. So, we have a paddle. So, this is called a paddle or a stirrer. So, shaft work is supplied to the paddle and the paddle is turned as you can see here and it ensures that the contents are maintained at the uniform temperature composition and so on. Now, we do not actually develop an expression for paddle work. Paddle work is either given or is an outcome of the analysis. So, we do not do anything more than that, but it is actually in our best interest to define the system in this manner because when you define the system in this manner what is that what crosses the system boundary is shaft work. In other words, we do not actually bother about how the paddle or how the work or the shaft work is transferred from the paddle to the gas inside. We do not worry about detail. We need not worry about details like that. If we define it like this, the only thing that crosses the system boundary is shaft work and we already have an expression for shaft work that we can use for the analysis. So, it is better to define the system in this manner for this particular situation. This concludes our discussion on work. So, we have looked at displacement work in great detail, tied it up to the definition of a system. We have looked at other forms of work also and that is about all we have to say on work. The next item that we take up is heat. In fact, heat is actually much easier to deal with because we do not even look at the details or develop any expression for heat. The heat transfer in the thermodynamic analysis is either given or you are asked to calculate it or in certain cases, we can take it to be zero because it is simply stated that there is no heat transfer. So, we take it to be zero. Nevertheless, we will just take a quick look at heat and heat transfer just to get an idea because some concepts from here will be essential later on when we start talking about heat transfer to engines and so on. So, heat transfer between two bodies takes place because of a temperature difference and a means of communication. So, there must be a temperature difference and there must be a means of communication between two bodies. If any one of them is absent, then heat transfer cannot take place. Heat is supplied to the system from a source which is at a higher temperature or heat is rejected by the system to a sink which is at a lower temperature. So, we can see that heat transfer always takes place from higher to lower temperature. So, when we supply heat to a system, we do so from a source at a higher temperature. When we reject heat from a system, we do so to a sink which is at a lower temperature than the system itself. In many engineering applications, the ambient is usually the sink to which heat is rejected. That is part of the problem or that is in fact, the problem which is which we are encountering today as devices operate and reject heat to the surroundings. Although the surroundings may be infinite, eventually after some point in time, temperature surroundings will begin to increase. So, we rejection of heat to the surroundings results in thermal pollution. In engineering thermodynamics, we are not actually interested in how this heat is transferred to the system. As I said before, the heat transferred to the system is either asked for or it is given to us. And the sign convention for heat is similar to what we did for work interaction. Remember, we are talking about engines. The engines are of interest to us in engineering thermodynamics. So, we supply heat to an engine so that it produces some useful work for us, which means that the sign convention for work is what done by a system is positive or done on the system is negative. Similarly, heat supplied to a system is positive, heat rejected by a system is negative or heat removed from a system is negative. That is the sign convention for heat. Now, once again depending on where we draw the system boundary, an interaction may be classified as heat interaction or work interaction. You may recall that we have insisted on the location of the system boundary because both heat and work or interactions of the system with the surroundings. The magnitude and sign of work as we have demonstrated before depends on where we draw the system boundary. Now, that becomes even broader depending on where we draw the boundary, something may be classified as a heat interaction or as a work interaction. So, for example, here we have a vessel in which there is a resistor. So, we supply current to the resistor and so the resistor undergoes omic heating and that heat is transferred to the gas or whatever is inside the vessel. Notice that there is no loss of heat from the vessel to the surrounding. So, this hatching indicates that the vessel is insulated and does not permit any transfer of heat across it. So, there is no heat going in or coming out from the ambient. So, here we supply heat due to omic heating, the temperature of the contents increase. So, when I draw a system like this which includes everything inside the vessel including the resistor, the only thing that crosses the system boundary is work and there is no heat interaction because we have an insulation. So, the heat interaction is zero and the work interaction is negative because electrical work is supplied to the system. When I do it like this, very clean, very simple, very nice. On the other hand, I may also choose to define a slightly more complicated system like this. So, this system includes just the gas, it excludes the resistor, but includes the gas in the vessel. For this system, notice that there is no work interaction because no part of the system boundary deforms, there is no shaft work, there is no electrical work. So, W is zero for this system. On the other hand, the omic heating from the resistor is actually transferred to the system. So, what is transferred, what crosses the system boundary in this case is heat. So, Q is positive. Remember, we are supplying heat to the system here. So, Q is positive and W is zero because no form of work interaction takes place for this system. So, this demonstrates clearly that depending on where we draw the system boundary, something may be classified as heat or work and depending on the manner in which we are supplying heat. So, which is why we laid such great emphasis on the definition of the system, looked at all the subtle aspects of the system and we went through so many examples to illustrate how to draw the system. So, before you begin any analysis, it is imperative to actually identify the system and then apply the equations to that system, integral PDV to that system, identify deforming parts of the system boundary, identify what crosses the system boundary, shaft work, electrical work, whatever, identify that and then go through the analysis. So, it is very, very important to define the system properly and keep track of the system boundary. So, let us summarize what we just said. Both heat and work are non-zero only when there is an interaction of the system with the surroundings. What is that? It is tempting and in fact, there is a misconception in this case that because there is omic heating and the contents are getting heated, there is a notion, misplaced notion that heat is supplied to the system. So, in this case, notice that heat does not cross the system boundary. Only work, electrical work crosses the system boundary. So, the heat transfer inside this vessel is inside the vessel that is not crossing the boundary. So, it cannot be classified as heat interaction. There is heat transferred between the resistor and the air or gas inside the vessel, but that is not a heat interaction of the system with the surroundings, which is a very important point. So, heat and work or non-zero only when the system interacts with the surroundings. If something, if heat transfer happens inside the system, that is not a heat interaction. So, any change that happens inside the system is only a conversion from one of the forms in which the system can store energy into another. So, basically, we are supplying electrical work and the electrical work is converted from work into temperature or energy of the system. So, that is what is taking place inside the system. What crosses the system boundary is what we define in thermodynamics as work or heat. So, one must be very, very careful with the terminology because heat is such a common terminology work is I mean work is such a common word, heat is such a common word used extensively. There is a danger that it can be misunderstood or misrepresented, but you must understand that in thermodynamics, both work and heat must cross the system boundary. So, what we will do in the next lecture is take up first law of thermodynamics for a system. So, we have not talked about work, we have not talked about heat, we will put both of these things together and write down first law of thermodynamics. So, work, heat and change in properties of the system is what we are going to discuss in the next lecture.