### Forms of the First Law of Thermodynamics

- Integral form of the first law (closed system):

$\Delta U + \Delta E_{k} + \Delta E_{p} = W + Q $

$\Delta u + \Delta e_{k} + \Delta e_{p} = w + q $

- Differential form of the first law (closed system):

$ dU + dE_{k} + dE_{p} = \delta W + \delta Q $

$du + de_{k} + de_{p} = \delta w + \delta q $

$ \frac{dU}{dt} + \frac{dE_{k}}{dt} + \frac{dE_{p}}{dt} =
\dot W + \dot Q $

$\frac{du}{dt} + \frac{de_{k}}{dt} + \frac{de_{p}}{dt} =
\dot w + \dot q $

##### Outcome:

Write the integral and differential forms of the first law

##### Outcome:

Describe the physical meaning of each of the terms within both
the integral and differential form of the first law

##### Outcome:

Determine when each term in the first law is zero or
negligible

##### Note:

We will often ignore changes in potential and kinetic energy.
Why?

##### Example:

If we assume that the stone from the previous example problem
lands in a puddle of water (10kg) at the bottom of the mine shaft,
and that the energy lost by the stone s completely used to heat the
water. What is the final temperature of the water if it started at
$20^\circ$C?