 Welcome back, we discuss another open system here, the pump. It is slightly different from the compressor in the sense we will use it to pump liquid to a higher pressure and liquids could be water or oil. And one of the assumptions that we make during this analysis is that the fluid the liquid that we are using is mostly going to be incompressible. Else we will have to have some kind of tables. Let us just look at the problem here at hand and see what we can do with it. Let me read it out. Feed water at 0.1 bar is pumped from a condenser into a boiler at 25 bar. Water at the exit of condenser is saturated and the compression is isentropic. Determine the work done per kilogram of water pumped. So, let us see how to approach this. As far as the first law for open system goes, this is reasonably straightforward to write down the equation. Still let me write down the equation here. We had q dot minus w dot s is equal to m dot h e minus h i plus v e squared by 2 minus v i squared by 2 plus g z e minus z i. And this is the pump. There is an inlet here. There is an exit here. This is the change in pressure. This is how we show it. So, inlet is given as 0.1 bar which is 0.01 megapascal. And this is a typical situation from a power plant where the exit of the condenser is saturated water and we need to pump it either at the boiler pressure or an intermediate pressure in between where it is mixed with some hot extraction from the turbine. So, here we know this is a 25 bar. So, the pump is assumed to be adiabatic. This is equal to 0 or assumed to be 0. We do not really expect the kinetic energies to change too much. So, as a reasonably good approximation, we put this equal to 0. Between the pump inlet and outlet, there may be some difference in heights, but that is really negligible. And we end up with our regular equation minus w dot s is m dot going into the pump h e minus h i. This is of course, the steady state equation. And if h e is greater than h i, what we get is that the work would be negative quantity. And this is what happens in the sense that we are putting in work into the pump and we get an increase in the enthalpy. Now, if the tables were listed well for water, then we would have got both h e and h i from the tables. But what we have right now is h i is well defined because it is at the saturated water state. So, this is well defined whereas, h e cannot be really found out from the tables unless there is a pretty good compressible water table available with you. So, if we just look at the situation here, if I draw it on a T s diagram, these are various isobars here. I will exaggerate it at this point. And we have a situation where the inlet is here and we pump it to a higher pressure here. So, this is P i, this is P e. So, really there is a change in temperature, but what we assume is that this fluid is incompressible and then P is the only quantity which is of significance which is changing here. And the specific volume does not change that is rho does not change. And though the diagram says that there is there may be some difference in T by our assumption delta T is negligible. In which case we just write down h e is u e plus P e v e h i is u i plus P i v i. If T does not change much then if I subtract h e minus h i, I will get u e minus u i plus P e v e minus P i v i. And what we have is that u e is equal to u i because T e is equal to P i by our assumption and h e minus h i will be just P e v e minus P i v i. And now even these two by our assumption they should be the same because the fluid is incompressible and we would just take it as v i P e minus P i. And this is one of the most common methods to get work transfer in a pump. Of course, if you have steam water table which tells you what the enthalpy is very well in the liquid state then you might as well use that otherwise this is a reasonably good approximation to go ahead with that is because the temperature does not change much. However, if the increase in pressure is really significant over 100 bar then the delta T would not be so small and it is better to look up the table if it is possible. Thank you.