Values of the second virial coefficient B of benzene and cyclohexane have been obtained from measurements of the excess molar enthalpy H-m(E) of {yN(2) + (1 - y)C6H6} and {yN(2) + (1 - y)C6H12} measured at standard atmospheric pressure over the temperature range 333.2 to 433.2 K. In a hypothetical mixture of an ideal gas with benzene or cyclohexane a measurement of H-m(E) is equivalent to a measurement of the isothermal Joule-Thomson coefficient phi 22 of the hydrocarbon. In a mixture of the nearly ideal gas nitrogen with hydrocarbon, phi(11) for nitrogen is small. The cross term isothermal Joule-Thomson coefficient phi(12) is also small and can be calculated with adequate accuracy using an established combining rule. Potential parameters which fit B-22 and phi(22) for the hydrocarbon can then be calculated from the H-m(E) measurements. It is shown that the H-m(E) measurements yield values of phi(22) for benzene and cyclohexane which are in good agreement with values obtained from throttling experiments, and that values of B-22 agree well with those obtained from (p, rho(n), T). It is suggested that H-m(E) measurements on these mixtures might be useful for testing the performance of mixing calorimeters, and empirical equations which fit the measurements at mole fraction y = 0.5 are given.