A system that converts thermal energy into mechanical energy. This is achieved by reducing the temperature of the working medium. The thermal energy of the medium at high temperature in the hot reservoir (`Q_H`) is converted to useful work (`W`) and the rest (`Q_C`) is left with the medium as it reaches a cooler temperature in the cold reservoir.
A system that converts thermal energy into mechanical energy. This is achieved by reducing the temperature of the working medium. The thermal energy of the medium at high temperature in the hot reservoir (`Q_H`) is converted to useful work (`W`) and the rest (`Q_L`) is left with the medium as it reaches a cooler temperature in the cold reservoir.
```
+Q_H -W -Q_C = 0
+Q_H -W -Q_L = 0
```
*Note: By convention, all variables indicate energy supplied **to** and work done **on** the system*.
More information at [Wikipedia][1].
### Efficiency
Efficiency is the ratio of useful work done *by* the system to energy provided *to* the system. For a heat engine:
@@ -25,59 +27,77 @@ Efficiency is the ratio of useful work done *by* the system to energy provided *
efficiency = -W / Q_H
```
## [Carnot's theorem][2]
An efficiency of 0.25 (1/4) means that one unit of work is done for 4 units of supplied energy.
More information on [thermal efficiency at Wikipedia][9].
## Carnot's theorem
The theorem puts the theoretical maximum limit on the efficiency of a *heat engine*. The greater the temperature difference between the hot (`T_hot`) and cold (`T_cold`) reservoirs, the higher the achievable efficiency. The maximum achievable efficiency is in a Carnot engine:
The theorem puts the theoretical maximum limit on the efficiency of a *heat engine*. The greater the temperature difference between the hot (`T_H`) and cold (`T_L`) reservoirs, the higher the achievable efficiency. The maximum achievable efficiency is in a Carnot engine:
```
efficiency <= 1 - T_cold / T_hot
efficiency <= 1 - T_L / T_H
```
## [Heat pump][7]
More information on [the theorem at Wikipedia][2].
A heat pump is a heat engine in reverse. It is a refrigerator. Work is done *on* the system to take energy supplied by the cold reservoir *to* the system and expel it *from* the system to the hot reservoir.
## Heat pump
A heat pump is a heat engine in reverse. Work is done *on* the system to take energy supplied by the cold reservoir *to* the system and expel it *from* the system to the hot reservoir.
```
+Q_C +W -Q_H = 0
+Q_L +W -Q_H = 0
```
More information at [hyperphysics][8].
## Coefficient of Performance (COP)
The COP measures the efficiency of a *heat pump*/*refrigerator*. It is defined as:
The COP measures the efficiency of an terms of useful energy *moved* relative to the amount of work done. For a heat pump, COP measures work required to move heat *into* the hot reservoir. For a refrigerator, COP measures work required to move heat *out of* the cold reservoir.
Because a heat pump is simply *moving* heat and not *creating* it from work, COP can - an does - exceed 1.
```
COP = Useful heat supplied (or removed) / Work done by the system
COP = Useful heat removed (or supplied) / Work done by the system
COP (cooling) = Q_C / -W
COP (cooling) = Q_L / -W
COP (heating) = -Q_H / -W = (-Q_C -W) / -W
COP (heating) = -Q_H / -W
```
The theoretical maximum COP for cooling is for a Carnot engine:
The theoretical maximum COP is for a Carnot cycle:
```
COP (max cooling): T_cold / (T_hot - T_cold)
COP (max cooling): T_L / (T_H - T_L)
COP (max heating): T_H / (T_H - T_L)
```
A `COP=4` for cooling means that a heat pump cools the cold reservoir by 4 units of heat energy using 1 unit of work to do so.
## [Wet-bulb temperature][3]
## Wet-bulb temperature
Temperature of a a thermometer wrapped in damp cloth over which air has passed and evaporative cooling has occcurred. With 100% humidity, no evaporation and hence no cooling occurs - therefore the wet bulb temperature is the same as dry-bulb/air temperature.
It is the lowest temperature that can be reached by evaporative cooling only under ambient conditions. Wet-bulb temperature is always less than or equal to ambient temperature.
Formulae for calculating wet-bulb temperature from ambient temperature and pressure can be found [here][7].
Formulae for calculating wet-bulb temperature from ambient temperature and pressure can be found [here][7]. More information at [Wikipedia][3].
## [Partial pressure][4]
## Partial pressure
It is the theoretical pressure of a gas if *only* it were occupying a container. The pressure of gas in a container is the sum of partial pressures of all constituent gases.
## [Equilibrium vapor pressure][5]
More information at [Wikipedia][4].
## Equilibrium vapor pressure
The pressure of vapor that is in thermodynamic equilibrium with its liquid state i.e. no net evaporation.
## [Relative humidity][6]
More information at [Wikipedia][5].
## Relative humidity
The ratio of partial pressure of water vapor to the equilibrium pressure of water vapor.
@@ -89,6 +109,8 @@ A 100% humidity (dewpoint) means that no net evaporation can occur because the a
For the same amount of water vapor, at higher temperatures the relative humidity decreases as the equilibrium pressure increases.
The purpose of this project is to analyze performance of HVAC systems - particularly chillers and cooling towers - in the Engineering Science Building (ESB) at Vanderbilt University.
These files document basics of HVAC systems and smart control approaches as they pertain to the scope of this research.
The purpose of this project is to analyze performance of HVAC systems - particularly chillers and cooling towers - in the Engineering Science Building (ESB) at Vanderbilt University to develop control approaches to maximize cooling and power efficiency.
The documentation is divided into a discussion of background concepts in physics, jargon in the HVAC industry, layout of air conditioning systems, and a description of the dataset specific to the system at ESB.
