 Welcome back. We are now going to look at exercise E09. Here we have to obtain an expression for a relation between Tp and H, partial of temperature with respect to pressure at constant H. This partial derivative is known as the Joule-Kelvin coefficient. You will appreciate the use of this when after this week, the remaining two weeks, you will study open thermodynamic systems. A constant enthalpy process for an unchanged enthalpy process represents to a large extent one of the processes in open systems, the throttling process. And the Joule-Kelvin coefficient tells us that when pressure reduces during a throttling process, what happens to the temperature? Whether it remains unchanged, in which case the Joule-Kelvin coefficient is 0 or when you reduce the pressure, does it increase, in which case the Joule-Kelvin coefficient is negative or when you reduce the pressure, the temperature also reduces. In that case, the Joule-Kelvin coefficient will be positive. Let us see how we go about deriving this expression. It is given to us that the Joule-Kelvin coefficient is defined as partial of T with respect to P at constant H. Now this constant H derivative is something which we have not come across earlier. All our partial derivatives were either at constant T, constant P, constant V or constant S. So what we do is we make use of the chain rule. The chain rule tells us that partial of T with respect to P at constant H multiplied by partial of P with respect to H at constant T multiplied by partial of H with respect to T at constant P is minus 1. And we immediately recognize that this is our specific heat at constant pressure Cp. And what we do now is transpose these two terms to the right hand side. So we get dT by dP at constant H is minus 1 over Cp into 1 divided by partial of P with respect to H at constant T. During the reciprocity relation we obtain this equal to 1 divided by Cp partial of H with respect to P at constant T. And for this term we have already derived a relation. So use that relation and your derivation will be complete. The end result is already shown to you in your exercise sheet. Thank you.