# FL: Forms of the First Law

### 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?