As shown in below Figure, the heat capacity of diamond near room temperature is approximately linear in T. Extrapolate this function up to 500 K, and estimate the change in entropy of a mole of diamond as its temperature is raised from 298 K to 500 K. Add on the tabulated value at 298 K (from the backof this book) to obtain S(500 K).

Figure: Measured heat capacities at constant pressure (data points) forone mole each of three different elemental solids. The solid curves show the heatcapacity at constant volume predicted by the model used in Section 7.5, with thehorizontal scale chosen to best fit the data for each substance. At sufficiently hightemperatures, CV for each material approaches the value 3R predicted by theequipartition theorem. The discrepancies between the data and the solid curvesat high T are mostly due to the differences between CP and CV. At T = 0 alldegrees of freedom are frozen out, so both CP and CV go to zero. Data from Y. S.Touloukian, ed., Thermophysical Properties of Matter (Plenum, New York, 1970).

INFO 1020: Analytics II Class Notes Mon. 1/25 Chapter 7a: Sampling and Sampling Distributions • Sampling Terminology • Population: Aset of ALL objects and corresponding data values for one variable - only ever one population • Sampling Frame: Asubset of the population which we use for the population when the population is not available...