 Welcome back. So we are now in a position to look at an illustrative example. The example problem concerns a balloon. It has an initial diameter of 0.2 meters, 20 centimeters and it is inflated using some gas and the initial pressure is 1.1 bar. It rises through the atmosphere and as it rises it expands. At the top of its flight its diameter is 0.4 meter. So it has doubled. The pressure of the gas is now 0.7 bar. Notice that the pressure has reduced. Assume that the pressure volume relation is linear that is a straight line on the pressure volume diagram. Determine the work done by the gas. So that is the specification of the problem. So the first thing we do is to sketch. Actually the sketching can be done as we read the problem. First we have a balloon. Since the diameter is given there is a volume associated with we assume that it is a spherical balloon. So the simple system diagram will be something like this. A spherical balloon. The gas inside the balloon with which we are concerned is our system. So this is the gas and that is our system. The initial state state 1 is given to us as diameter of 0.2 meter. Pressure of the gas as 1.1 bar. The final state let us call it state 2 is given to us as diameter 0.4 meter and pressure of 0.7 bar. We are also told that the pressure volume relationship is linear. So if you sketch the pressure volume relationship. So the volume will go from V1 to V2. The pressure will go down from P1 to P2. So the initial state will be this. State 1. The final state will be this. State 2. And we are told that the pressure volume relationship is a straight line. So let me sketch the process as a straight line from state 1 to state 2. And from this diagram it is clear to us that it is a quasi-static process and hence this area is going to represent the pressure volume work, the expansion work. So this is the first step in the problem.