Outside air generally contains some water vapor (typically 1-2% by mass). Does it take more, less, or the same heat to raise the temperature of 1kg moist air than is needed to raise the temperature of 1kg dry air by the same amount?

Since the molecular weight of water vapor is 18 and that of air is 29 (the N2/O2 weighted average), the presence of H2O vapor therefor lowers the average molecular weight of air. 1 kg of dry air will have fewer moles than 1 kg of moist air.

It will take more energy to heat the gas with more moles (moist air)

Water vapor has a higher molar specific heat (than O2 and N2) as well, but the fact that there will be more moles in the same mass of moist air is what makes the biggest difference

To determine if it takes more, less, or the same amount of heat to raise the temperature of 1kg of moist air compared to 1kg of dry air, we need to consider the specific heat capacity of each component.

1. Dry Air: Dry air consists mostly of nitrogen, oxygen, and other trace gases. The specific heat capacity of dry air at constant pressure (Cp) is approximately 1005 J/(kg·K).

2. Water Vapor: Water vapor, being a different substance than dry air, has its own specific heat capacity at constant pressure (Cp). The specific heat capacity of water vapor is approximately 1990 J/(kg·K).

Now, let's calculate the total heat required to raise the temperature of 1kg of each type of air by the same amount (let's assume 1 Kelvin for simplicity).

For 1kg of dry air: heat = mass × specific heat capacity × temperature change
Heat required = 1kg × 1005 J/(kg·K) × 1K = 1005 J

For 1kg of moist air: We need to account for both the dry air and the water vapor.
Heat required = (mass of dry air × specific heat capacity of dry air + mass of water vapor × specific heat capacity of water vapor) × temperature change

Given that outside air typically contains 1-2% of water vapor by mass, let's assume it contains 1% water vapor. This means 99% of the 1kg of moist air is dry air, and 1% is water vapor.

Mass of dry air = 1kg × 99% = 0.99kg
Mass of water vapor = 1kg × 1% = 0.01kg

Heat required = (0.99kg × 1005 J/(kg·K) + 0.01kg × 1990 J/(kg·K)) × 1K
Heat required = (994.95J + 19.9J) = 1014.85 J

Comparing the two values, we find that it takes slightly more heat (approximately 1.5%) to raise the temperature of 1kg of moist air by 1K compared to 1kg of dry air by the same amount.

Therefore, it takes more heat to raise the temperature of 1kg of moist air than is needed to raise the temperature of 1kg of dry air by the same amount.