212man has it right. To put it another way, I think it is the first law of thermodynamics which says energy can be neither created or destroyed, merely changed in form. To compress a gas you need to imput energy (don’t you work up a sweat pumping up a tyre with a hand pump). When that gas is allowed to expand (back to ambient in the case of bleed air heater) that gas retains the heat (energy) required to originally compress that gas (ignoring any losses). Allied to this is that the N1 turbine/compressor system is about 98% efficient. That is, the turbine recovers 98% (approx) of the energy required by the compressor.