When balloons carrying people first took to the skies in the eighteenth century, they stimulated a lot of interest in the properties of gases. Calculate the final temperature and the change in enthalpy when 500. J of energy is transferred as heat to 0.900 mol O₂ (g) at 298 K and 1.00 atm at

(a) Constant pressure;

(b) Constant volume. Treat the gas as ideal.

ANTICIPATE You should expect the temperature to rise more as a result of heating at constant volume than at constant pressure, because at constant pressure some of the energy is used to do expansion work. That, in turn, suggests that the increase in enthalpy might be greater at constant volume than at constant pressure.

PLAN Oxygen is a linear molecule, and its heat capacities can be estimated from the equipartition theorem; then, use q = CΔT, with C = nC_V,m or nC_P,m for the changes at constant volume and constant pressure, respectively, to find the changes in temperature.

The enthalpy change at constant pressure is equal to the heat supplied. At constant volume, find the enthalpy change by calculating ΔU and then converting it to ΔH by using ΔH = ΔU + nRΔT.

What should you assume? Assume that oxygen behaves as an ideal gas and that there is no vibrational contribution to the heat capacity.