Cloud formation Air consists mostly of nitrogen (N2), with a molecular mass of 28, a...

Cloud formation Air consists mostly of nitrogen (N₂), with a molecular mass of 28, and oxygen (O₂), with a molecular mass of 32. A water molecule (H₂O) has molecular mass 18. According to the ideal gas law (N/V = P/kT), dry air at a particular pressure and temperature has the same particle density (number of particles per unit volume) as humid air at the same pressure and temperature. Consequently, humid air, whose low-mass water molecules replace more massive nitrogen and oxygen molecules, is less dense than dry air—the humid air rises. Atmospheric pressure decreases with elevation since there is less air above that is pushing down. At about 5000 m above the Earth’s surface, the pressure is about 0.5 atm. Assuming an ideal gas, the gas volume V increases as pressure P decreases. What happens to the air temperature as humid air rises? Air is a poor thermal energy conductor, and there is little heating from neighboring air (Q = 0, an adiabatic expansion process). As the rising gas expands, the neighboring environmental gas pushes in the opposite direction of the increasing volume of this rising gas. The environment does negative work on the rising air system (W _{by Environment on System} < 0). According to the first law of thermodynamics The system’s internal thermal energy decreases with a corresponding temperature decrease—about -10 °C for each 1000-m increase in altitude. When the humid air reaches its dew point temperature, it starts to condense into water droplets (cloud formation). When condensation occurs, energy is released. There is a competition between decreasing thermal energy as the air expands and increasing thermal energy as the water vapor condenses. The air now cools at a lower rate of about -5 °C for each 1000-m increase in elevation.

If no condensation occurred, how high would 40 °C humid air have to rise before its temperature decreased to 10 °C?

(a) 1000 m (b) 2000 m (c) 3000 m

(d) 6000 m (e) 10,000 m