We've come to the end of week 5, a full week, a lot of material mostly devoted to the first law of thermodynamics. So I'd like to finish then, with a review of what I think the high points were. So, stated in words, the first law of thermodynamics most simply would be, energy is conserved. And mathematically, we go beyond that to express dU is equal to delta q plus delta w. Where u is the internal energy, q is the heat, and w is work. And there are conventions for the signs of heat and work. By convention, heat is positive when it's absorbed by the system. Work is positive when it's done on the system, and vise versa. Energy is a state function. That is, it depends only on the variables defining the state, temperature, pressure, number of particles, for instance. Heat and work on the other hand are path functions. The amount of heat or work that changes depends on how you go from one state point to another state point. Work, when it's done by expanding a gas, is equal to minus the external pressure times dv, the change in volume. Where p ext is, indeed, the external pressure against which the gas expands. A reversible process is one that happens in infinitesimally small steps. And the maximum work that can be extracted from the isothermal expansion of a gas, is the reversible work. Where the external pressure is going to be equal to the pressure of the ideal gas itself. Another term that we define is an adiabatic process. Adiabatic implies that the heat transfer delta q is equal to 0. And under those circumstances, since du is equal to delta w, and since u is a state function, W is also a state function for an adiabatic process. If you expand a gas adiabatically against an external pressure it must cool. Another state function is enthalpy. Enthalpy is written capital H. It's defined as the sum of the internal energy plus pressure times volume. Delta H for a constant pressure process, is equal to the heat transferred at constant pressure, which is represented by putting a p as a subscript on q. That also leads to a definition for a constant pressure heat capacity. And that's defined as the change in enthalpy with respect to the change in temperature at a constant pressure. Another way of thinking of it, is the amount of heat that's required to raise the temperature of the substance by one degree. For an ideal gas, the difference between the heat capacity at constant pressure Cp, and the heat capacity at constant volume Cv, when we talk about the molar quantities, they differ by r. So the Cp is greater than Cv by r. Enthalpy itself can be measured, or most more accurately enthalpy changes can be measured. And in particular, if you want to talk about the change in enthalpy as you go from absolute zero to some non-zero temperature, that's computed by looking at the heat capacity as a function of temperature, which since it's a measurement of how much heat is required to raise the temperature by one degree, you can measure that degree by degree. And when you integrate all of that heat that has been transferred, of course that's all contributing to the enthalpy. That integration gives you the enthalpy change, and then when there are phase transitions between say a solid and a liquid, or a liquid and a gas phase, additional heat is required. That's defined as the heat of fusion, or the heat of vaporization, integration of the heat capacities for the various phases, also contributes as you get up to the next phase change. And that allows you then to, through experiment define the enthalpy at a given temperature relative to that at zero. And I showed an example that I've just re-capitulated here in these slides for the case of benzene. So, these are the measured heat capacities, these are the integrated heat capacities which is the enthalpy. Enthalpy being a state function that implies that it is a additive property, and so that leads to the convenient Hess' Law. Which says if you'd like to know the enthalpy change for a given reaction, if you can construct that reaction out of other reactions, adding them or subtracting them, for which you know the heat of reaction, then that unknown one will be the sum of those various other reactions. Standard enthalpy of reactions, unlike Just a general enthalpy of reaction which is an extensive process it depends on how much you have a standard enthalpy of reaction is intensive. It refers to one mole of a certain specified quantity, and such standard enthalpies are tabulated for defined standard states where definition requires a choice of convention. And in particular that convention is that the standard molar enthalpy of formation for a pure element, in its most stable form, at a given temperature, is defined to have a heat of formation of zero. And given that definition, looking at the changes in enthalpy as you transform pure elements into chemical compounds Allows you to define the heat of formation for those chemical compounds. Given heats of formation and heat capacities, one can then determine, as long as all of the participants in a chemical reaction have known heats of formation and heat capacities, One can determine the enthalpy change for that process, as the heat of formation of the products minus the heat of formation of the reactant. That's sufficient if you already have tabulated data for the temperature you're interested in. If the temperature of interest for the reaction is not the same as that the heats of formation are tabulated for. That's when you can use the difference in heat capacities of products versus reactants to add to that an integrated term from the temperature you know to the temperature of interest, in order again to determine the heat of reaction at the final temperature. So a lot of tools that are now in our toolbox. That allow us to, understand changes in energy, changes in work, changes in heat and changes in enthalpy. That wraps up what I think are the most important points in week five. We're going to move on from the first law of thermodynamics next week. We're going to address a new state function and a key thermodynamic property, and that is entropy. I look forward to seeing you then.