Sigma heat, denoted

S

, is a measure of the

specific energy Specific energy or massic energy is energy per unit mass. It is also sometimes called gravimetric energy density, which is not to be confused with energy density, which is defined as energy per unit volume. It is used to quantify, for example, sto ...

of humid air. It is used in the field of

mining engineering Mining in the engineering discipline is the extraction of minerals from underneath, open pit, above or on the ground. Mining engineering is associated with many other disciplines, such as mineral processing, exploration, excavation, geology, and ...

for calculations relating to the temperature regulation of mine air. Sigma heat is sometimes called ''total heat'', although total heat may instead mean

enthalpy Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...

Definition

Sigma heat is the energy which would be extracted from a unit mass of humid air if it were cooled to a certain reference temperature under constant pressure while simultaneously removing any

condensation Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor to ...

formed during the process. Because sigma heat assumes that condensation will be removed, any energy which would be extracted by cooling the water vapor below its condensation point does not count towards sigma heat. The reference temperature is usually , although is sometimes used as well. Assuming a reference temperature of 0°F, the following formula may be used under standard temperature ranges and pressure:Different temperature ranges or pressures will slightly alter the

heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity i ...

of the water vapor and the air, causing a deviation from the accuracy of this formula.

S = 0.24 \mathrm t + W \;( 0.45 \mathrm t + 1061 \mathrm )

:where :

S

is the sigma heat of the air (in BTU/lb), :

t

is the

dry-bulb temperature The dry-bulb temperature (DBT) is the temperature of air measured by a thermometer freely exposed to the air, but shielded from radiation and moisture. DBT is the temperature that is usually thought of as air temperature, and it is the true ther ...

of the air (in °F), and :

W

is the

specific humidity Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present. Humidity depe ...

of the air (unitless). The equivalent metric formula:

S = 17.86 \mathrm + 1.005 \mathrm t + W \;( 2501 \mathrm + 1.884 \mathrm t)

:where :

S

is the sigma heat of the air (in kJ/kg), :

t

is the

of the air (in °C), and :

W

is the

of the air (unitless) sometimes expressed as kg/kg.

Comparison with enthalpy

Sigma heat is not the same as the

of the humid air above the reference temperature. (Enthalpy is sometimes called ''total heat'' or ''true total heat'') Unlike sigma heat, enthalpy does include the energy which would be extracted in cooling the condensed water vapor all the way to the reference temperature. Essentially, enthalpy assumes that ''all'' components of the system must be cooled during the cooling process, whereas sigma heat assumes that some of those components (liquid water) are removed part way through the process. Nevertheless, some writers mistakenly use the term enthalpy when they actually mean sigma heat, creating some confusion. Assuming a reference temperature of 0°F, the relationship between enthalpy and sigma heat may be shown mathematically as:

h = S + 1 \mathrm W t'

:where :

h

is the specific enthalpy of the air above its reference temperature, :

S

is the sigma heat of the air (in BTU/lb), :

W

is the

of the air (unitless), and :

t'

is the wet bulb temperature (in °F). :(Standard temperature ranges are assumed.)

Wet bulb temperature vs. dry bulb temperature

Assuming constant pressure, sigma heat is solely a function of the

wet bulb temperature The wet-bulb temperature (WBT) is the temperature read by a thermometer covered in water-soaked (water at ambient temperature) cloth (a wet-bulb thermometer) over which air is passed. At 100% relative humidity, the wet-bulb temperature is equal ...

of the air. For this reason,

humidity Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present. Humidity depe ...

need not be taken into account unless

measurements are used. Like sigma heat, the wet bulb temperature is not directly affected by the temperature of any condensed water vapor (liquid water), and it varies only when there is a net energy change to the system. In contrast, the dry bulb temperature can vary even for processes where there is no such net energy change. This difference may be understood by examining

evaporative cooling An evaporative cooler (also known as evaporative air conditioner, swamp cooler, swamp box, desert cooler and wet air cooler) is a device that cools air through the evaporation of water. Evaporative cooling differs from other air conditioning sy ...

. During evaporative cooling, all energy lost from air molecules as

sensible heat Sensible heat is heat exchanged by a body or thermodynamic system in which the exchange of heat changes the temperature of the body or system, and some macroscopic variables of the body or system, but leaves unchanged certain other macroscopic vari ...

is gained as

latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process — usually a first-order phase transition. Latent heat can be understo ...

by water molecules evaporating into that air. With no

net energy gain Net Energy Gain (NEG) is a concept used in energy economics that refers to the difference between the energy expended to harvest an energy source and the amount of energy gained from that harvest. The net energy gain, which can be expressed in jo ...

ed or lost from the now more humid air, sigma heat remains unchanged. In keeping with this, the wet bulb temperature also remains unchanged, as its reading already represented the maximum possible amount of evaporative cooling. The dry bulb temperature however is in conflict with the sigma heat since it decreases during such evaporative cooling. This is why measurements of sigma heat which use dry bulb temperatures must also take into account the humidity of the air.

Notes

References

{{cbignore, bot=medic Mining engineering Psychrometrics Heating, ventilation, and air conditioning