The heat capacities and Joule-Thomson coefficients have been evaluated using three known analytical expressions for radial distribution functions (RDFs). Using such approach not only tests the power of distribution functions theory in predicting the heat capacities and Joule-Thomson coefficients, but also specifies better expressions in determining these properties. To calculate these quantities, the variation of RDF with density and temperature is required. Therefore, we should have analytical expressions which explicitly present RDF as a function of temperature, density, and interparticle distance. It is shown that if an expression is used which properly presents RDFs as a function of interparticle distance, density, and temperature, it is possible to calculate heat capacities and Joule-Thomson coefficients from distribution function theory.