Subsections

### 5 Processes

#### 5.1 Control Mass Processes (Closed Systems)

Specific heat and work:

Continuity (mass conservation):

The first law of thermo (energy conservation):

Work:

In case of an ideal gas, note that can be replaced by .

Exams 3 and final only
More generally:

The second law for reversible adiabatic (isentropic) processes:

The second law of thermo for general processes:

End exams 3 and final only

#### 5.2 Rate Equations

The first law as a rate equation:

Work as a rate equation:

For an ideal gas:

For liquids and solids:

#### 5.3 Steady State Control Volume Processes

The control volume is assumed to be steady state in all formulae below.

Specific work output and heat added (i.e., per unit mass flowing through):

In- and outflow velocities and pipe cross-sectional areas:

(where is velocity.)

Continuity (mass conservation):

where means sum over all inflow, respectively outflow, points, if there is more than one.

The first law of thermo (energy conservation):

The kinetic energy and potential energy terms are often ignored. Devices without moving parts do not do work, . Adiabatic devices have no heat transfer, .

Exams 3 and final only

The second law of thermo for a reversible adiabatic (isentropic) process inside a single entrance and exit CV:

The second law of thermo for a reversible isothermal process inside a single entrance and exit CV:

The second law for a general control volume:

Specific work done during a reversible process inside a single entrance and exit CV:

where

In case of an ideal gas, note that can be replaced by .

Special case of (a) ideal gas, (2) polytropic, , (including isentropic constant specific heats, then ,) and (3) reversible:

Special case of (a) ideal gas, (2) constant specific heats, (3) polytropic, (isothermal). and (4) reversible: