# TP: Work and Energy

### 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

$dW = FdL = MgdL = Mgh$