When I'm doing the Physics homework the problem for heat of vaporization uses Q=mcΔT and Q=mLv. How do I know when to use which equation through out the problem?
The first formula is related to a change in temperature (hence the presence of ##\Delta T##), when a single phase is heated, while the second is related to the phase transition at constant temperature.
Problems usually ask to make calculations going from ##T_1## to ##T_2##, with a phase transition somewhere in there, ##T_1 < T_t < T_2##. You then need to calculate for instance the heat in the liquid phase from ##T_1## to ##T_t##, then the latent heat of vaporization, then heat in the gas phase from ##T_t## to ##T_2##.