A narrow Gaussian excluded volume potential, which tends to a delta-function repulsive potential in the limit of a width parameter d* going to zero, has been used to examine the universal consequences of excluded volume interactions on the equilibrium and linear viscoelastic properties of dilute polymer solutions. Brownian dynamics simulations data, acquired for chains of finite length, have been extrapolated to the limit of infinite chain length to obtain model-independent predictions. The success of the method in predicting well-known aspects of static solution properties suggests that it can be used as a systematic means by which the influence of solvent quality on both equilibrium and nonequilibrium properties can be studied.