First Law of Thermodynamics
Q = DE + Wfor a closed system,
where Q is the heat transferred into the system, W is the work done by, or taken out, of the system, and DE is the increase in the internal energy E of the system.
Note that this precludes the possibility of "perpetual motion" machines, whose work output is always greater than the work obtained by converting the heat put into them. At some point, there will be no more internal energy available to convert to work.
Derivation of the Energy Equation for a Control Volume
We can also relate the rates of heat transfer, energy change, and work as:
Consider each of these rates for a control volume in a fluid:
where is the mass flow rate out of the control surface through its surface, and e is the energy per unit mass of the fluid.
where is specific volume (volume per unit mass), and is the power taken out through shear forces and through rotating shafts.
The energy per unit mass of the fluid can be written as
where eint is internal energy, u is speed, and P.E. is potential energy per unit mass. Thus,
where the integral is taken over the surface of the control volume.Now
,the enthalpy per unit mass.
can be written as , andcan be written as
where is the component of the velocity directed outward from the surface of the control volume.