### Work and Energy

Recall that Thermo began as a way to evaluate the potential of
steam engines. In other words, the goal was to ascertain how much
work could be extracted from a given system.

##### Definition:

**Work** is the action of a force over a distance.
In other words, moving stuff is doing work.

$dW = F dL = -PA d(\frac{AL}{A}) = -P dV$

##### note:

The pressure has no direction thing is the origin of the - sign;
specifically, since moving something requires *input* of work we
need to calculate the work to compress something (which would cause
a dV<0) in such a way as to give us a positive work.

##### note:

The - sign ensures that compressive work (where dV<0) is
positive.

Energy has the same units as work and can be thought of as
somethings's ability to perform work (if you like).

##### Definition:

**Kinetic energy** follows naturally from Newton's
Law and can be thought of as energy related to motion:

$dW = F dL = Ma dL = M (\frac{du}{dt}) dL = M
(\frac{dL}{dt}) du = M u du$

integrating gives:

$W = \frac{1}{2} M \Delta (u^2)$

##### Definition:

**Potential energy** can be thought of as energy
related to position

$dW = FdL = MgdL = Mgh$