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.


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

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


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.


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).


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:

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


Potential energy can be thought of as energy related to position

$dW = FdL = MgdL = Mgh$