In a hot-air balloon launch and flight, temperature being unchanged would keep the pressure variable constant, while the volume would change due to temperature and pressure fluctuations.
In the context of a hot-air balloon launch and flight, if the temperature remains unchanged, the variable that would remain constant is temperature in the compound gas law. When no heat transfer occurs, the temperature inside the balloon would remain stable, affecting the other variables.
According to Amontons's Law, when a rigid container of gas is heated, the pressure of the gas increases. Therefore, if the pressure inside the balloon were to stay consistent during the flight, then the pressure variable would remain unchanged.
As for the volume of the balloon, it would not remain constant during the launch and flight, as changes in temperature and pressure can affect the volume of the gas inside the balloon.
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