i only know 1): Q = mc delta T refers to heat energy released or absorbed into a system. enthalpy, on the other hand, is defined as delta H = delta U + delta PV. in simple words, U is the energy currently in the system, and delta P V is the product of the change in pressure and volume, which can kind of be thought of as the work that is required to expand the system from V =0 to the current V against the pressure on the system (someone probably has a better explanation for this, i might be wrong). now if the change in pressure is 0, then we just get delta H= delta U. and by the first law of thermodynamics, delta u = Q - W, but we established that if delta PV = 0, then the "work" term becomes 0, so we assume that W = delta PV =0. so now delta H = Q = mc delta T. in other words, when something is at a constant pressure and volume, then the change of enthalpy is exactly equal to the change in heat energy into the system.