Q.The variation of volume V, with temperature T, keeping pressure constant is called the coefficient of thermal expansion i.e. $\alpha=\dfrac{1}{V}\left(\dfrac{\partial V}{\partial T}\right)_P$. For an ideal gas $\alpha$ is equal to

Hot air balloons work on the volume-temperature relationship of gases (V proportional to absolute/Kelvin temperature at constant pressure).

When the air inside a hot air balloon is heated by the burner, its pressure stays close to the surrounding atmospheric pressure (the balloon envelope is open at the bottom), so at constant pressure its volume increases in direct proportion to its absolute (Kelvin) temperature. Because the same mass of air now occupies a larger volume, its density falls below that of the cooler air outside, and the resulting buoyant force lifts the balloon — this is exactly the gas law that relates volume to the Kelvin temperature scale.

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