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The level of free convection is the altitude in the atmosphere where the temperature of the environment decreases faster than the moist adiabatic lapse rate of saturated air parcel at the same level. The usual way of finding LFC is to lift parcel from lower level along dry adiabatic lapse rate until it crosses saturated mixing ratio line of parcel: this is lift condensation level. From there on, follow the moist adiabatic lapse rate until the temperature of the parcel reaches air mass temperature, at equilibrium level. If the temperature of parcel along moist adiabat is warmer than the environment on further lift, one has found LFC. Since the volume of parcel is larger than surrounding air after LFC by ideal gas law, it is less dense and becomes buoyant rising until its temperature equals surrounding airmass. If the airmass has one or many LFC, it is potentially unstable and may lead to convective clouds like cumulus and thunderstorms.
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