A balloon is launched at sea level, where the air pressure is \(100 \mathrm{kPa}\). The density in the hot-air chamber is \(1.0 \mathrm{~kg} / \mathrm{m}^{3}\). What is the density of the air when the balloon has risen to a height where the atmospheric pressure is \(33 \mathrm{kPa}\) ?

A. \(3.0 \mathrm{~kg} / \mathrm{m}^{3}\)

B. \(1.0 \mathrm{~kg} / \mathrm{m}^{3}\)

C. \(0.66 \mathrm{~kg} / \mathrm{m}^{3}\)

D. \(0.33 \mathrm{~kg} / \mathrm{m}^{3}\)

Long-distance balloon flights are usually made using a hot-airballoon/helium-balloon hybrid. The balloon has a sealed, flexible chamber of helium gas that expands or contracts to keep the helium pressure approximately equal to the air pressure outside. The helium chamber sits on top of an open (that is, air can enter or leave), constant-volume chamber of propane-heated air. Assume that the hot air and the helium are kept at a constant temperature by burning propane.