[BLANK_AUDIO]. In this video, I shall present the third law of thermodynamics, and show how it enables determination of absolute entropy. The third law of thermodynamics states that the entropy of any perfect crystal at absolute zero is a well-defined constant. This constant value at zero kelvin is defined as zero on the entropy scale. Thus, the entropy of a perfect crystal at zero kelvin is zero. From this definition of the zero point on the entropy scale, we can now determine absolute entropy, and hence standard molar entropies. Imagine an infinitesimal amount of heat, delta Q reversible is supplied reversibly to an object. The resulting entropy change, delta S, is calculated according to the definition of entropy, as delta S equals delta q rev divided by T. The heat capacity of the object is defined as delta q rev divided by delta T. And thus, delta q rev equals the heat capacity, multiplied by delta t. Substituting this back in our equation for the change in the entropy gives delta s equals the heat capacity, multiplied by delta t divided by temperature. If the temperature changes from Ti, the initial temperature, to Tf, the final temperature, then delta S equals the integral between Ti and Tf of CdT over T. If we assume that the heat capacity is constant over the range of temperature, then we can bring the heat capacity outside the integral. The integral of dx over x is a standard integral and is equal to log x plus c. Thus, the integral of dT over T is log T. Putting the limits in gives us delta S equals C multiplied by log Tf minus log Ti. We now use the logarithm identity shown on the right, to get the final result, the delta s equals c log tf over ti, show as equation 15. Thus, entropy can be determined by measurement of the heat capacity as a function of temperature. Once the graph of heat capacity versus temperature has been determined, it needs to be replotted as heat capacity divided by temperature, versus temperature, and then the area under the graph between two temperatures, calculated from equation 15, is the entropy change between those two temperatures. To determine absolute entropies, this process needs to be carried out for all temperatures, from zero kelvin up to whatever the desired standard temperature happens to be. Two problems present themselves: First, there will be discontinuities in the heat capacity graph at melting and boiling points. At these points it will be necessary to add the entropy diffusion and vaporization. Also, measurement of heat capacity very close to zero Kelvin is extremely difficult. An example of how this problem can be overcome is the Debye T cube law, which enables us to approximate heat capacities of non-metallic substances at constant volume, by the molar heat capacity at constant volume equals a T cubed. Slide eight shows tabulated standard molar entropies at 298 K. The substances have been grouped in the order, gases, liquids, then solids. What you should notice is that gasses generally have higher entropies than liquids, which have higher entropies than solids. This should hopefully make sense if you consider the molecular motion of atoms and molecules in solids, liquids and gasses. Another point of interest is that even changes in solid structure impact on entropy. Graphite, which comprises honeycomb sheets of carbon atoms separated by layers of electrons, has a higher entropy than diamond, which is a three dimensional array of tetrahedrally bonded carbon atoms. In graphite, the layers can slide over one another, and this flexibility leads to the higher entropy value. Okay, so now we have covered all four laws of thermodynamics, and defined a good number of state functions. In the next and final lecture we shall examine how an intrinsic property of state functions leads to Hess' law and see a series of examples of Hess' law calculations [BLANK_AUDIO].