 Welcome back. We are now at a stage we can consider solving some problems using the first law of thermodynamics. Of course, we have looked at only a few types of working fluids. In particular, we have looked at the ideal gas. You will soon be provided with a set of exercises to do using the first law of thermodynamics. And in the immediate set of exercises, the working fluid would invariably be an ideal gas. But let us look at something which we have to consider and keep in mind when we do problem solving and invoke the first law of thermodynamics. Remember that when you do this, you have to remember what type of system it is. Currently we will be looking at only closed systems, but it could be open. Then we have to look at the type of working fluid that is the contents of the system. And in particular, we have to look at its equation of state and we have to look at its energy relation. For an ideal gas, for example, the equation of state would invariably be PV equals RT. And the basic in energy relation would be du is CV dt, the ideal gas law based on the Boyle's law and the definition of CV based on the Joule's law. Then we have to look at processes. Now, in a particular exercise, it is possible that only one type of process is involved or it is possible in a more complicated situation that a series of different processes are involved. Now we know one classification of process as either quasi-static or non-quasi-static. This is one specification and we know that quasi-static processes would be amenable to analysis by integration because we know everything intermediate from the initial state to the final state. Whereas for non-quasi-static processes, we do not know intermediate states. We hardly have any information other than the initial state and the final state. Apart from this, we will have other specifications and let us look at these specifications now. Apart from the qualification quasi-static and non-quasi-static, in particular if a process is quasi-static, we can have a type of specification which indicates the path in state space. Let us take some example. Let us consider what we may usually call an isobaric process. This is generally known as a constant pressure process. That is why the technical name is isobaric. For such a process p, the pressure is uniform throughout, uniform and constant. And this also means that through the process if we want to analyze it in detail, the differential of the pressure would be 0 throughout the process. And hence, if you consider say a pv depiction of the state space, an isobaric process would be something like this. The initial state 1 and the final state 2 would be at the same pressure. The isobaric process would be a process in which the pressure does not change. So this is an illustration of an isobaric process from the initial state 1 to a final state 2. And remember that the pressure does not change from its initial value throughout the process. We should not confuse a pair of isobaric states from an isobaric process. For example, in this illustration, the initial state and the final state are two states which are isobaric. That means p1 equals p2. The process 1 to 2 is isobaric as shown in this figure because throughout the process the pressure maintains its initial value. But here I will now show two states, state 1 and state 2. These two are isobaric states because they have the same pressure. However, I can have a process which goes say something like this. It is a quasi-static process from the initial state 1 to the final state 2. However, it is not an isobaric process. This should be clear the difference between saying that a pair of states is isobaric as in 1, 2 here or 1, 2 in the earlier figure. And a process is isobaric. In this figure on the left hand side, the process 1 to 2 is an isobaric process. Here dp equals 0 at any stage during the process. Here dp need not be 0 at any stage during the process. In a similar way, we will have another illustration of an isobaric process. Isobaric in normal English means constant volume. And this means v is maintained constant throughout the process and hence dv will be 0 throughout our process. A depiction of such a process would be on a pv diagram. This is an illustration of an isobaric process. In a similar fashion as explained earlier, here are a pair of states 1 and 2 which are like 1 and 2 here. A pair of isochoric states. Whereas you can consider a process like this or may be even a process like this. Both these processes 1, a2 and 1, b2, neither of them are isochoric. Continuing with our discussion, the third type of process which we may come across quite often is an isothermal process. This means constant temperature. And that also means not only is the temperature constant throughout the process, it also means dt equals 0 throughout the process. Unlike the earlier processes, for example, without worrying about the type of system, we could have the isobaric process, a process which is such that the pressure is uniform constant throughout by horizontal line on the pv diagram. Similarly, a constant volume process would be a vertical line on the pv diagram. We do not have to worry about the type of fluid, whether it is an ideal gas, whether it is a solid, liquid, some other complicated gas, does not matter. However, when it comes to an isothermal process, it depends on the type of fluid. And the depictions for different types of fluids would be different. I will just take an illustration of an ideal gas. So here, our example system contains an ideal gas. For an ideal gas, the isotherm is represented by a rectangular hyperbola. So if we start our isothermal process from state 1, we may end up with state 2. This is an isothermal process. But remember that this isothermal process as depicted on this diagram is essentially for an ideal gas. If the gas does not behave like an ideal gas, the process depictions may well be different. Here again, the initial state and the final state are a pair of isothermal states. I will leave it to you as an exercise to sketch a situation where the initial state and the final state are a pair of isothermal states. But the process is not an isothermal process. In general, the word iso can be used for a process in which some property is maintained constant. For example, we can have an isofi process where the property phi is constant throughout the process and hence d phi, the differential of phi is 0 throughout the process. If phi is volume, it is an isochoric process. If phi is pressure, it is an isobaric process. If phi is temperature, it is an isothermal process. If you consider phi to be enthalpy, it could be an iso enthalpy process and so on. You can select your favorite property or the appropriate property and you can have iso that property process. There is another type of important specification and which is an adiabatic process. Now, remember by definition an adiabatic process is one which has only work type of interaction. However, by the definition of heat interaction, it immediately means that an adiabatic process does not have any heat interaction. That means dq any time during the process is 0 at any stage during the process and hence it implies that for an adiabatic process, this is the basic definition and the first consequence is that the heat transfer to or from the system is 0. Notice that an adiabatic process does not mean anything other than this and this. An adiabatic process only means that in the first law, the general expression for which for a closed system is q equals delta E plus w, we will put this equal to 0 for an adiabatic process and hence delta E plus w will be 0 for an adiabatic. It means nothing more, nothing less. And because of this, we should remember that an adiabatic process does not have a unique representation in state space. Because it does not say anything about property, it specifies an interaction. In particular, it specifies that there is no heat interaction and this can be in principle combined with a process which is isobaric. So you could have an isobaric and adiabatic process. Process could be constant volume, so you could have an adiabatic isochoric process. In a similar fashion, it is not impossible to have an adiabatic isothermal process. We will soon see an illustration of a particular adiabatic process. Thank you.