# Temperature

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Temperature, abbreviated as T or TEMP, is normally described as the amount of heat or cold, but it is neither heat or cold.  Temperature is expressed as a number that is related to energy and porportional to a type of energy, but it is not energy.  Temperature is a number related to the average kineric energy, but is not kinetic energy.  Temperature is a scalar quantity having direction, some of these include area, density, energy, entropy, length, mass, power, pressure, speed, volume, and work.

Temperature is the measurement of the average speed of molecules that are moving around in an object.  Molecules don't always travel at the same speed.  The faster they move the hotter they get, the slower they move the colder they get.  When they stop moving that is absolute zero.  Temperature is measured in celsius, fahrenheit, kelvin, and rankine.

In piping design, temperature is important because mechanical properties are affected by increases or decreases in temperature.  Most materials become more pliable as the tempearture increases.  For pressurized pipe, this means that ability to contain the pressure is decreased.  In very low temperatures and cryogenic services, the material become brittle and can fracture if it is involved in a high vibration environment.  Additionally, as temperature increases and decreases, materials will expand and contract.  Carbon steel, for example, expands at a rate of about 1 inch per 100 feet per 100 degrees Ferenheit.  Long sections of pipe without expansion loops can look like spaghetti and come off their supports.  Concrete without provisions for expansion can buckle and fracture.  Large pressure vessels such as heater treaters should have one end "floating" to allow for expansion.

## Temperature formula

$$\large{ T = \frac{ T_d \; - \; 112 \; \left( \frac{ RH }{ 100 } \right)^{\frac{1}{8}} \; + \; 112 }{ 0.9 \; \left( \frac{ RH }{ 100 } \right)^{\frac{1}{8}} \; + \; 0.1 } }$$
Symbol English Metric
$$\large{ T }$$ = temperature $$\large{ F }$$   $$\large{ K }$$
$$\large{ T_d }$$ = dewpoint temperature $$\large{ F }$$ $$\large{ K }$$
$$\large{ RH }$$ = relative humidity $$\large{ F }$$ $$\large{ K }$$

## Related Temperature formulas

$$\large{ T = \frac{ B }{ A\;-\; log_{10} \;p } -C }$$    (Antoine equation)

$$\large{ T = \frac {p \; V}{n \; R} }$$     (Ideal Gas Law

$$\large{ T = \frac {p }{\rho \; R} }$$     (IDeal Gas Law

Symbol English Metric
$$\large{ T }$$ = temperature $$\large{ T }$$ $$\large{ T }$$
$$\large{ \rho }$$  (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ n }$$ = mole $$\large{ mol }$$ $$\large{ mol }$$
$$\large{ p }$$ = pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{ Pa }$$
$$\large{ e_s }$$ = saturated vapor pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{\frac{kg}{m-s^2}}$$
$$\large{ R }$$ = specific gas constant $$\large{\frac{ft-lbf}{lbm-R}}$$  $$\large{\frac{J}{kg-K}}$$
$$\large{ p }$$ = vapor pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{ Pa }$$
$$\large{ V }$$ = volume $$\large{in^3}$$ $$\large{mm^3}$$

## Absolute Temperature

Absolute temperature, abbreviated as $$T_a$$, also called thermodynamic temperature, is measured from the starting point of 0, where zero is the coldest theoretically attainable temperature in nature.  It is the lowest temperature possible and contains no heat energy in the substance.  Absolute temperature is directly related to Zeroth Law of Thermodynamics.

## Absolute Zero

Absolute zero is the temperature at which all motion within molecules completely stops.  Below absolute zero temperature does not exist.  At this temperature nothing is in motion.

## Ambient Temperature

When outdoors the ambient temperature is the current surrounding environment air temperature.  This temperature has nothing to do with high or low forcasts.

When inside the ambient temperature is the room temperature and can be affected by many factors such as humidity, insulation, HVAC equipment, people, the outside temperature, and etc.

## Bulk Temperature

Bulk temperature, abbreviated as $$T_b$$ or $$\bar {F}$$, also called average bulk temperature, is the average temperature of a cross section of a mixture of fluid leaving or entering the flow in pipe and ducts.  It can be used for evaluating heat reansfer or heat transfer rate.

## Condensing Temperature

All air containes different amounts of water, the condensate temperature is the point at which water vapor returns to its origional liquid state.

## Dew Point

Dew point is the temperature at which air must be cooled to become saturated with water vapor.  It is porportional to the amount of water vapor in a given amount of air and when the dew point is raised the more water vapor present, also the opposite.

## Rated Temperature Rise

The allowable rise in temperature above ambient when operating under load.

## Temperature Examples

 Explanation Celsius Fahrenheit Kelvin Rankine Boiling Point of Water 100.00 212.00 373.15 671.67 Triple Point of Water 0.01 32.03 273.16 491.69 Freezing Point of Water at Sea Level 0.00 32.00 273.15 491.67 Absolute Zero - 273.15 - 459.67 0.00 0.00

## Temperature Typical Units

Common units for temperature are as follows:

INTERNATIONAL SYSTEM OF UNITS, SI

ENGLISH UNITS

Celsius Farenheit
Kelvin Rankine

## Temperature Conversion

### Celcius to Farenheit

$$\large{ C = 5/9 \;(F - 32) }$$

$$\large{ F = 9/5 \;(C + 32) }$$

### Celcius to Kelvin

$$\large{ K = C - 273.15 }$$

$$\large{ C = K + 273.15 }$$

### Farenheit to Rankine

$$\large{ R = F - 459.67 }$$

$$\large{ F = R + 459.67 }$$

## Celsius

Celsius, abbreviated as C, is a unit of temperature most commonly used through out the world.

## CELSIUS FORMULAs

$$\large{ T_{°C} = \frac {T_ {°F} \;-\; 32°}{1.8} }$$

$$\large{ T_{°C} = 273.15° - T_ {°K} }$$

$$\large{ T_{°C} = \left( \frac {T_{°R}} {1.8} \right) - 273.15° }$$

Symbol English Metric
$$\large{ T }$$ = temperature $$\large{ T }$$  $$\large{ T }$$
$$\large{ C }$$ = celsius - $$\large{ C }$$
$$\large{ F }$$ = fahrenheit $$\large{ F }$$ -
$$\large{ K }$$ = kelvin - $$\large{ K }$$
$$\large{ R }$$ = rankine $$\large{ R }$$ -

## Fahrenheit

Fahrenheit, abbreviated as F, is a unit of temperature used in the United States and a few other countries.  Celsius is most commonly used through the world.

## FAHRENHEIT FORMULAs

$$\large{ T_{°F} = 32° + \left( \frac{9}{5} \right) T_ {°C} }$$

$$\large{ T_{°F} = 459.67° - \left( \frac{9}{5} \right) T_ {°K} }$$

$$\large{ T_{°F} = 459.67° - T_ {°R} }$$

Symbol English Metric
$$\large{ T }$$ = temperature $$\large{ T }$$  $$\large{ T }$$
$$\large{ C }$$ = celsius - $$\large{ C }$$
$$\large{ F }$$ = fahrenheit $$\large{ F }$$ -
$$\large{ K }$$ = kelvin - $$\large{ K }$$
$$\large{ R }$$ = rankine $$\large{ R }$$ -

## Kelvin

Kelvin, abbreviated as K, is a unit of temperature normally used for scientific calculations.  Unlike celsius, fahrenheit and rankine, the word degree is not used.  Since Kelvin starts with absolute zero it has no negative numbers.

## Kelvin FORMULAs

$$\large{ T_{ °K} =273.15 ° + T_ { °C} }$$

$$\large{ T_{ °K} = \frac {T_ { °F} \;+\; 459.67°}{1.8} }$$

$$\large{ T_{°K} = \frac {T_{ °R}} {1.8} }$$

Symbol English Metric
$$\large{ T }$$ = temperature $$\large{ T }$$  $$\large{ T }$$
$$\large{ C }$$ = celsius - $$\large{ C }$$
$$\large{ F }$$ = fahrenheit $$\large{ F }$$ -
$$\large{ K }$$ = kelvin - $$\large{ K }$$
$$\large{ R }$$ = rankine $$\large{ R }$$ -

## Rankine

Rankine, abbreviated as R, is a unit of temperature used in the US engineering field.  0 is set at absolute zero.

## Rankine FORMULAs

$$\large{ T_{°R} = \left(273.15° + T_ { °C} \right ) \; 1.8 }$$

$$\large{ T_{°R} = 459.67° + T_ { °F} }$$

$$\large{ T_{°R} = \left( T_{°K} \right) \;1.8 }$$

Symbol English Metric
$$\large{ T }$$ = temperature $$\large{ T }$$  $$\large{ T }$$
$$\large{ C }$$ = celsius - $$\large{ C }$$
$$\large{ F }$$ = fahrenheit $$\large{ F }$$ -
$$\large{ K }$$ = kelvin - $$\large{ K }$$
$$\large{ R }$$ = rankine $$\large{ R }$$ -

## Temperature Instruments

In piping design, temperature is measured several different ways.  On a Piping & Instrumentation Diagram, the typical instruments are:

Thermowell - Thermowells are used in temperature measurement and provide isolation from the temperature sensor and the process fluid.  This is important because the temperature element is usually a piece of wire or wires that need to be in the process.  It provides not only structural integrity but also protection to the temperature element.

Temperature Element - A temperature element is a piece of wire, such as an Resistance Tempearture Detector (RTD), that provides the input to a temperature transmitter or temperature switch.

Temperature Indicator - A tempearture indicator is a temperature gauge.  It is a mechanical device, that contains two dissimilar pieces of metal joined together.  Each piece of metal has a different coefficient of expansion.  This difference is calculated to turn a shaft to display the temperature of the process.

Temperature Transmitter or Temperature Indicating Transmitter - This is used to display the temperature in the equipment and send an analog signal to a computer for futher processing.  It might be used as an alarm in case the temperature gets outside normal operating conditions.

Temperature Switch - A temperature switch is used to send a digital signal (yes or no, 1 or 0) to a computer for an action to be performed.  E.g. send an alarm, turn off a pump, etc.