The first is rather
obvious, if the thermodynamic system under consideration does mechanical work
then U must decrease in order for the total energy to be conserved:
Here it is crucial to remember the sign convention employed. We have chosen a
convention by which dW is the work performed by the thermodynamic
system. The reason for this is that in the processes which we shall
consider later the goal is to extract mechanical work from
a thermodynamic system and so with our sign conventions
dW will generally be positive. In mechanics we learned that
The force exerted by the thermodynamic system is
so that the expression for dW becomes
