The classical second virial coefficient and its first two quantum corrections are evaluated for a repulsive exponential potential by the use of Laplace transforms. The results are used to estimate the effect of the intermolecular attraction in the high‐temperature second virial coefficient of4He and in its first quantum correction. An approximation is found for this first quantum correction at temperatures above 100°K for4He. A simplified expression for theS‐wave phase shift of the exponential repulsion is derived and is used to calculate a quantum‐mechanical turning point for wave packets or effective hard core radius. Similar methods are applied to the Morse potential to evaluate the classical second virial coefficient and its first quantum correction and theS‐wave phase shift.