 Welcome. We now look at the first of the two interactions that we are going to study, the work interaction. The idea of work is a primitive in thermodynamics. It is defined in other branches of physics. For example, it is defined in mechanics and electricity, magnetism, fluid mechanics and so on. The basic idea of work, if you look at the mechanical definition, is we have a force and we have a displacement. If the point of application of the force moves in the direction of the displacement, then we have the work being done. Since we have a force as a vector, displacement is also a vector, we have to have a dot product here, so that the component of displacement in the direction of force or the component of force in the direction of displacement is taken into account. The other branches of physics also define it in somewhat similar way, except that we can have a sort of a generalized force and a generalized displacement. Let us consider some examples and we will now look at it from a thermodynamic point of view, so we will have a system and we will have another system for a surroundings. And for us, work interaction has to be energy in transit, so there has to be a proper interaction between the system and the surroundings. Let us take one illustration. Let us say that we have a rod or if you wish you could even consider it to be a spring and let us say that there is a loop at the end of it and we have a somebody or something which is pulling it. Let us say that this rod is our system and it is pulled by someone, say my hand and because of it being pulled, there is a tension in the rod, the rod pulls me back and let the tension be t, tension is a force and because of my pull, let us say that the initial length of the rod is l and it gets extended by a small amount dL. So I am holding something in my hand like a rod and I am pulling it and because I pull it, it gets extended a bit. Of course the pencil is too stiff to get extended but I could use a spring and extend it a bit. Now in this particular case, the system is the rod of the spring and the small amount of work done is minus t dL, where t is the tension so we have something like a force here and we have the displacement dL. We will see and discuss this negative sign later. Let us take another example. All of us have a mobile phone and each mobile phone has a battery in it or the chargeable cell. So let us say that we have such a chargeable cell here. Let us say that it has a positive terminal and it has a negative terminal. Let us say that the cell is our system. Let us have a connection from the positive terminal and the negative terminal and let the potential, electric potential be E of the positive terminal with respect to negative terminal. This could be 1.5 volts, 2 volts, 3 volts depending on the type of cell that we have. And let us say that these terminals are connected to some load. It could be the circuit of the mobile phone. It could be a simple resistor, a small lamp and let us say that this circuit consumes a charge dQ. Now charge is conserved. So whatever is the charge taken from the positive terminal has to be returned to the negative terminal. In terms of i, the current, if the current is i, this will be the current into the small amount of time dt during which the current flows. And we know that in this case, we will say that the work done by our system will be plus E dQ or if you want to write it as it will be plus E i dt. Notice the plus sign here. Another illustration which we will look at is some reasonably thick liquid. So the system is some liquid and what we have is a stirrer dipped inside it and what we do is we try to rotate the stirrer by a small angle d theta. The liquid is thick. It is viscous. It could be very viscous like condensed milk. You know how difficult it is to stir condensed milk. But if you try to stir it, the liquid imposes a torque opposing the stirrer which we have to overcome. Let the torque be tau. In this case, the system is the liquid and we now say that the work done is minus tau d theta. Again notice that there is a negative sign here. Let us take one more example. Let us consider a typical cylinder piston arrangement. And let us say that the piston for simplicity a leak proof frictionless piston encloses some fluid say a gas inside it. So the system is the gas in this cylinder piston arrangement. Let us say that the pressure of the gas is P and this acts uniformly on the piston. Let the area of the piston be A, area of the piston exposed to the fluid. And because of this the force which is acting on the piston presence of the fluid is P into A. And let us say that the piston is initially held in place because of an equivalent opposite force being applied from the outside. Maybe I am holding it so that it does not fly off. And if I relax myself a bit, the piston will move by a distance dx. That is the displacement of the piston. And now we will say that for our system which is the gas in this cylinder piston arrangement, the work done will be the force into the displacement. The force is P into A into dx. And since area and displacement when multiplied give you the change in the volume of the system, this becomes P dv. So in this particular case the work done by the gaseous system is P dv. And in particular we can write it as plus P dv if we are conscious of the sign.