###
Definitions of Heat and Work

Both heat and work have intuitive definitions. However, we need to
forego those as we study thermodynamics, because they can be misleading
if not used carefully. To that end, we will rigorously define both
concepts here.

Heat is the transfer of energy to a system via thermal contact with
a reservoir. Work is the transfer of energy to a system via a
change in the parameters of the system, such as volume.

This seemingly small distinction has significant consequences. Remember
that a transfer of energy from a reservoir must obey the thermodynamic
identity (taken for constant N and V), *dU* = *τ* *dσ*. Therefore a
change in energy, i.e. a heat transfer, is accompanied by an
entropy transfer. The addition of work,
however, can't change the entropy of the system since we are only
changing the external environment of the system.

We can look at the thermodynamic identity in a new way. The first term,
*τ* *dσ*, can be thought of as the heat input, written *dQ*. The
second term, - *p* *dV*, can be thought of as the work input, written
*dW*. The third term, *μ* *dN*, can be thought of as the chemical work
input, written *dW*_{c}. Therefore the total change in energy is due
entirely to the sum of the heat inputted, work, and chemical work done
on the system.

###
Heat Engines

We need to think of entropy in a new way, though it is yet the same
fundamentally as before. Entropy cannot build up indefinitely in a
system. If it is introduced accompanying some heat input, it must
eventually be released from the system.

This restriction does not affect the conversion of work into work,
however. A plant that converts the rush of a river into electricity
does not have to worry about entropy. Similarly, conversion of work
into heat does not lead to a buildup of entropy. Conversion of heat to
work, however, the basic process of a heat engine, must be done
carefully to avoid buildup of entropy.