# State number

The dimensionless number of states describes the ratio of a gas volume in the normal state to the gas volume in the operating state. ${\ displaystyle Z}$

## definition

${\ displaystyle Z = {\ frac {V_ {n}} {V_ {B}}} = {\ frac {T_ {n}} {T}} \ cdot {\ frac {p_ {amb} + p_ {e} - \ varphi \ cdot p_ {s}} {p_ {n}}} \ cdot {\ frac {1} {K}}}$

Mean:

• ${\ displaystyle V_ {n}}$= Standard volume
• ${\ displaystyle V_ {B}}$= Operating volume, d. H. Volume in the operating state
• ${\ displaystyle T_ {n}}$= Standard temperature (273.15  Kelvin , corresponds to 0 ° C)
• ${\ displaystyle T}$= mean operating temperature of the gas in Kelvin (for gas meters without temperature measurement set to 288.15 Kelvin or 15 ° C)
• ${\ displaystyle p_ {n}}$= Standard air pressure (1 013.25 hPa or 1 013.25 mbar or 1.01325 bar)
• ${\ displaystyle p_ {amb}}$= Annual mean value of the air pressure (in Pascal ):${\ displaystyle p_ {amb} = 1016 \, {\ text {hPa}} - 0 {,} 12 \, {\ frac {\ text {hPa}} {\ text {m}}} \ cdot h}$
• ${\ displaystyle h}$= geodetic height (in m)
• ${\ displaystyle 0 {,} 12 \, {\ frac {\ text {hPa}} {\ text {m}}}}$see air pressure gradient
• ${\ displaystyle p_ {e}}$= Operating pressure or effective pressure of the gas ( overpressure in Pascal)
• ${\ displaystyle \ varphi \ cdot p_ {s}}$= Water vapor partial pressure of the gas (in Pascal)
• ${\ displaystyle K}$= Number of compressibility (dimensionless; at )${\ displaystyle K = 1}$${\ displaystyle p_ {e} \ leq 1000 \ \ mathrm {hPa}}$

## use

The state number is used by gas supply companies to calculate the amount of thermal energy actually extracted in kilowatt hours . The operating volume determined on the gas meter from the meter reading difference is first multiplied by the status number. The standard volume determined in this way is then multiplied by the calorific value:

{\ displaystyle {\ begin {aligned} E & = V_ {B} \ times Z \ times H_ {S, n} \\ & = V_ {n} \ times H_ {S, n} \ end {aligned}}}

Mean:

• ${\ displaystyle E}$= Amount of energy (in )${\ displaystyle \ mathrm {kWh}}$
• ${\ displaystyle V_ {B}}$= Gas volume in operating state (in )${\ displaystyle \ mathrm {m ^ {3}}}$
• ${\ displaystyle V_ {n}}$= Standard volume, d. H. Gas volume in standard condition (in )${\ displaystyle \ mathrm {m ^ {3}}}$
• ${\ displaystyle H_ {S, n}}$= mean calorific value in standard condition (in ).${\ displaystyle \ mathrm {kWh / m ^ {3}}}$

## example

Calculation of the state number for natural gas customers in Munich, in the district of Thalkirchen-Obersendling-Forstenried-Fürstenried-Solln
with the values:

{\ displaystyle {\ begin {aligned} h & = 562 \, {\ text {m}} \\\ Rightarrow p_ {amb} & = 1016 \, {\ text {hPa}} - 0 {,} 12 \, { \ frac {\ text {hPa}} {\ text {m}}} \ cdot 562 \, {\ text {m}} = 948 {,} 6 \, {\ text {hPa}} \\ p_ {e} & = 24 \, {\ text {hPa}} \\\ varphi \ cdot p_ {s} & = 0 \, {\ text {hPa}} \\ K & = 1 \ end {aligned}}}

This gives the state number:

{\ displaystyle {\ begin {aligned} \ Rightarrow Z & = {\ frac {273 {,} 15 \, {\ text {K}}} {288 {,} 15 \, {\ text {K}}}} \ cdot {\ frac {949 \, {\ text {hPa}} + 24 \, {\ text {hPa}} + 0 \, {\ text {hPa}}} {1013 {,} 25 \, {\ text { hPa}}}} \ cdot \, {\ frac {1} {1}} \\ & = 0 {,} 9103 \ end {aligned}}}

## literature

• Ulrich Wernekinck (Ed.): Gas measurement and gas billing. 3rd edition, Vulkan Verlag, Essen 2005, ISBN 978-3-8027-5617-7 .
• Knut Håkansson: Lexicon of the gas installation. (Gas installation from A - Z), 2nd edition, Vulkan Verlag, Essen 1996, ISBN 3-8027-2533-6 .

## Individual evidence

1. Procedure for determining the condition number and billing calorific value (PDF; 23 kB) website of SWM Infrastruktur GmbH, accessed on October 6, 2014