Residual Volume (rv) is important because it prevents the lungs from collapsing. It also prevents the inside surfaces of the lungs touching, thus creating friction. It also prevents the inner surfaces of the lungs sticking together.
Another reason why we have a residual volume is that gaseous exchange is continuously occurring so after we have expelled as much air as possible (expiratory reserve volume) gaseous exchange is still occurring.
Residual volume can be shown in this equation:
residual volume = inspiratory reserve volume - tidal volume - expiratory reserve volume
for an average person residual volume will be around 1 to 1.5 litres.
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A residual volume is important, cause it keeps the alveoli open for further gaseous exchange.
It is also helpful in maintaining the proper respiration in the body of a person if he/she gets cut off from oxygen supply.
And we can even say that according to osmosis the molecules travels from high concentrated area to low concentrated area for that purpose there should be a regular opening in exchanging site. For that reason this air (residual volume) is present in the lungs which never allows the alveoli to close.