Final answer:
The density of the gas in a hot-air balloon is less than the atmosphere outside due to the higher temperature inside, which can be calculated using the ideal gas law. pH is not relevant to the measure of density in dry air. Lifting capacity is determined by the difference in mass between cooler displaced air and the heated air inside the balloon.
Step-by-step explanation:
The density of the gas in a hot-air balloon is related to the air temperature inside the balloon. The density of hot air inside the balloon is less than the density of the cooler atmosphere outside because hot air is less dense than cool air at the same pressure. Under standard conditions (STP), the density of dry air is 1.2256 g/L. The density inside a hot-air balloon can be calculated using the ideal gas law, taking into account that the average temperature inside the balloon is higher than the temperature of the atmosphere.
When the air inside the balloon is heated to 120°C (or 393 K), the density decreases because the air expands. The average molar mass of dry air can be calculated based on the composition of air which is 78% N2, 21% O2, and 1% Ar. This calculation does not directly involve the pH of the air; pH is a measure of acidity and is not applicable to dry air.
For a hot-air balloon with a specified volume, the lifting capacity can be calculated by taking the difference in mass between the displaced cool air and the heated air inside the balloon. The calculation of lifting power also involves the consideration of the weight of the balloon and its rigging. The balloon's capacity for carrying passengers and cargo is determined by the difference in weight between the overall lifting power and the weight of the balloon and rigging.