Clapeyron's equation calculator
Calculations related to Clapeyron's equation known also as ideal gas law. Enter known values (e.g. pressure and temperature) and select which value you want to find out (e.g. volume) and we'll show you step-by-step how to transform basic formula and reach your result in desired units.

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# Symbolic algebra

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# What do you want to calculate today?#

 Choose a scenario that best fits your needs I know number of moles (n), temperature (T) and volume (V) and want to calculate pressure (p)I know number of moles (n), temperature (T) and pressure (p) and want to calculate volume (V)I know pressure (p), volume (V) and temperature (T) and want to calculate number of moles (n)I know pressure (p), volume (V) and number of moles (n) and want to calculate temperature (T)

# Calculations data - enter values, that you know here#

 Pressure (p) yottapascal [YPa]zettapascal [ZPa]exapascal [EPa]petapascal [PPa]terapascal [TPa]gigapascal [GPa]megapascal [MPa]kilopascal [kPa]hektopascal [hPa]pascal [Pa]decipascal [dPa]centipascal [cPa]milipascal [mPa]micropascal [µPa]nanopascal [nPa]pikopascal [pPa]femtopascal [fPa]attopascal [aPa]zeptopascal [zPa]yoctopascal [yPa]centimeter mercury (0°C) [cmHg]milimeter mercury (0°C) [mmHg]inch mercury (32°F) [inHg]inch mercury (60°F) [inHg]centimeter water (4°C) [cmAq]milimeter water (4°C) [mmAq]inch water (4°C) [inAq]foot water (4°C) [ftAq]inch water (60°F) [inAq]foot water (60°F) [ftAq]newton per square meter [N/m²]newton per square decimeter [N/dm²]newton per square centimeter [N/cm²]newton per square milimeter [N/mm²]dyne per square centimeter [dyne/cm²]technical atmosphere [at]kilogram-force per square meter [kgf/m²]kilogram-force per square centimeter [kgf/cm²]kilogram-force per square milimeter [kgf/mm²]gram-force per square centimeter [gf/cm²]ton-force (long) per square inch [tf(long)/in²]ton-force (short) per square inch [tf(short)/in²]kip-force per square inch [kip/in²]ksi [ksi]ton-force (long) per square foot [tf(long)/ft²]ton-force (short) per square foot [tf(short)/ft²]pound-force per square foot [lbf/in²]psi [psi]pound-force per square foot [lbf/ft²]poundal per square foot [pdl/ft²]bar [bar]milibar [mbar]microbar [µbar]Torr [Tr]standard atmosphere [atm] <= Volume (V) cubic yottameter [Ym³]cubic zettameter [Zm³]cubic exameter [Em³]cubic petameter [Pm³]cubic terameter [Tm³]cubic gigameter [Gm³]cubic megameter [Mm³]cubic kilometer [km³]cubic hektometer [hm³]cubic meter [m³]cubic decimeter [dm³]cubic centimeter [cm³]cubic milimeter [mm³]cubic micrometer [µm³]cubic nanometer [nm³]cubic picometer [pm³]cubic femtometer [fm³]cubic attometer [am³]cubic zeptometer [zm³]cubic yoctometer [ym³]gigalitre [Gl]megalitre [Ml]kilolitre [kl]hectolitre [hl]litre [l]decilitre [dl]centilitre [cl]mililitre [ml]microlitre [µl]nanolitre [nl]picolitre [pl]femtolitre [fl]attolitre [al]lambda [λ]drop (metric)drop (medical)cubic angstroms [Å³]cubic mile [cu mi]acre-foot [ac ft]acre-inch [ac in]cubic fathom [cu fm]cubic foot [cu ft]cubic yard [cu yd]perch [per]cubic inch [cu in]hogshead [hhd]barrel (petroleum) [bl, bbl]barrel [fl bl]gallon [gal(US)]fifthquart [qt]pint [pt]gill [gi(US)]fluid once [US fl oz]fluid dram, fluidram [fl dr]jiggershotponypinchminim [min]dashdrop [gtt]drop (alt) [gtt]weyseambarrel [bl]strikesackbushel (heaped) [bu]bushel (level) [bu (lvl)]firkinpeck [pk]gallon [gal]quart [qt]pint [pt]lastwater tonhogshead [hhd]seam, pailbarrel [bl]coombsack, bag [bag]kilderkinstrikebushel [bu]bucket [bkt]peck [pk]gallon [gal]pottle, quarternquart [qt]pint [pt]fluid once [fl oz]gill, noggin [gi]fluid drachm [fl dr]fluid scruple [fl s]pinchdashdrop [gtt]drop (alt) [gtt]minim [min]register ton [RT]load unitfreight ton [FT]displacement ton [DT]cord (firewood)cord-foottimber footboard-foot [fbm]Cup (Canadian) [c]Tablespoon (Canadian) [tbsp]Teaspoon (Canadian) [tsp]Cup (Imp) [c]Breakfast cup (Imp)Tablespoon (Imp) [tbsp]Teaspoon (Imp) [tsp]Dessert spoon (Imp)Cup (US) [c]Tablespoon (US) [tbsp]Teaspoon (US) [tsp]Cup (Metric)Tablespoon (Metric)Teaspoon (Metric)tunbutt, pipebeer gallon [beer gal] => Number of moles (n) yottamole [Ymol]zettamole [Zmol]examole [Emol]petamole [Pmol]teramole [Tmol]gigamole [Gmol]megamole [Mmol]kilomole [kmol]hektomole [hmol]mole [mol]decimole [dmol]centimole [cmol]milimole [mmol]micromole [µmol]nanomole [nmol]pikomole [pmol]femtomole [fmol]attomole [amol]zeptomole [zmol]yoctomole [ymol]number of particles [particles] <= Temperature (T) Kelvin [K]degree Celsius [°C]degree Fahrenheit [°F]degree Rankine [°R, °Ra]degree Delisle [°De]degree Newton [°N]degree Réaumur [°Ré]degree Rømer [°Rø] <=

# Units normalization#

 Number of moles (n) Show source$1\ \left[mol\right]$ Temperature (T) Show source$0\ \left[^\circ C\right]\ =\ \frac{5463}{20}\ \left[K\right]$ Volume (V) Pressure (p) Show source$1013.25\ \left[hPa\right]\ =\ 101325\ \left[Pa\right]$

# Result: Volume (V)#

Summary
Used formulaShow source$\mathrm{V}=\frac{n \cdot R \cdot \mathrm{T}}{p}$
ResultShow source$\frac{1821}{675500}~R$
Numerical resultShow source$22.41396207863582531458179126572908956328645447816432272390821614\ \left[dm^3\right]$
Result step by step
 1 Show source$\frac{1~R \cdot \frac{5463}{20}}{101325}$ Multiply by one Any number multiplied by one (1) gives the same number: $a \cdot 1 = 1 \cdot a = a$ 2 Show source$\frac{R \cdot \frac{5463}{20}}{101325}$ Removed double fractional mark Divide by fraction is the same as multiply by fraction inverse: $\frac{a}{\frac{c}{b}} = a \cdot \frac{b}{c} = \frac{a \cdot b}{c}$ 3 Show source$\frac{R \cdot 5463}{101325 \cdot 20}$ Simplify arithmetic - 4 Show source$\frac{R \cdot \cancel{5463}}{\cancel{2026500}}$ Cancel terms or fractions Dividing a number by itself gives one, colloquially we say that such numbers "cancel-out": $\frac{\cancel{a}}{\cancel{a}} = 1$to find-out the simplest form of fraction we can divide the numerator and denominator by the greatest common divisor (GCD) of both numbers. 5 Show source$\frac{1}{675500} \cdot R \cdot 1821$ Multipled fractions To multiply two fractions we need to multiply numberators and denominators from first and second fractions: $\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$ 6 Show source$\frac{1 \cdot 1821}{675500} \cdot R$ Multipled fractions To multiply two fractions we need to multiply numberators and denominators from first and second fractions: $\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$ 7 Show source$\frac{1 \cdot 1821~R}{675500}$ Multiply by one Any number multiplied by one (1) gives the same number: $a \cdot 1 = 1 \cdot a = a$ 8 Show source$\frac{1821~R}{675500}$ Rearrange coefficients Multiplication and addition are commutative. Due to this property, we can change arguments order to get better readability of expression. 9 Show source$\frac{1821}{675500}~R$ Result Your expression reduced to the simplest form known to us.
Numerical result step by step
 1 Show source$0.02241396207863582531458179126572908956328645447816432272390821614$ The original expression - 2 Show source$0.02241396207863582531458179126572908956328645447816432272390821614$ Result Your expression reduced to the simplest form known to us.
Units normalization
Show source$0.02241396207863582531458179126572908956328645447816432272390821614\ \left[m^3\right]\ =\ 22.41396207863582531458179126572908956328645447816432272390821614\ \left[dm^3\right]$

# Some facts#

• The perfect gas (also known as ideal gas) is a hypothetical, simplified model approximating the behavior of real gases. A perfect gas is different from the real one, in that its molecules do not interact with each other.
• More formally, we say that the perfect gas does not take intermolecular interactions into account.
• The ideal gas law was first formulated in 1834 by Benoîta Clapeyron. For this reason, it is also known as the Clapeyron equation.
• The ideal gas state equation is usually written in the following form:
$pV = nRT$
where:
• The Clapeyron equation was originally a generalization (synthesis) of the then known empirical laws describing in a rough way the behavior of gases:
• the Boyls law - the gas pressure is inversely proportional to the volume:
$p \propto \dfrac{1}{V}$
• the Charles law - the volume of gas is directly proportional to the temperature:
$V \propto T$
• the Avogadro law - the volume of gas is directly proportional to the number of moles of gas in the vessel:
$V \propto n$
• the Gay-Lussac law - the gas pressure is directly proportional to the temperature:
$p \propto T$

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