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

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

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Calculations data - enter values, that you know here#

Pressure (p)
<=
Volume (V)
=>
Number of moles (n)
<=
Temperature (T)
<=

Units normalization#

Number of moles (n)Show source1 [mol]1\ \left[mol\right]
Temperature (T)Show source0 [C] = 546320 [K]0\ \left[^\circ C\right]\ =\ \frac{5463}{20}\ \left[K\right]
Volume (V)
Pressure (p)Show source1013.25 [hPa] = 101325 [Pa]1013.25\ \left[hPa\right]\ =\ 101325\ \left[Pa\right]

Result: Volume (V)#

Summary
Used formulaShow sourceV=nRTp\mathrm{V}=\frac{n \cdot R \cdot \mathrm{T}}{p}
ResultShow source1821675500 R\frac{1821}{675500}~R
Numerical resultShow source22.41396207863582531458179126572908956328645447816432272390821614 [dm3]22.41396207863582531458179126572908956328645447816432272390821614\ \left[dm^3\right]
Result step by step
1Show source1 R546320101325\frac{1~R \cdot \frac{5463}{20}}{101325}Multiply by oneAny number multiplied by one (1) gives the same number: a1=1a=aa \cdot 1 = 1 \cdot a = a
2Show sourceR546320101325\frac{R \cdot \frac{5463}{20}}{101325}Removed double fractional markDivide by fraction is the same as multiply by fraction inverse: acb=abc=abc\frac{a}{\frac{c}{b}} = a \cdot \frac{b}{c} = \frac{a \cdot b}{c}
3Show sourceR546310132520\frac{R \cdot 5463}{101325 \cdot 20}Simplify arithmetic-
4Show sourceR54632026500\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": aa=1 \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.
5Show source1675500R1821\frac{1}{675500} \cdot R \cdot 1821Multipled fractionsTo multiply two fractions we need to multiply numberators and denominators from first and second fractions: abcd=acbd\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}
6Show source11821675500R\frac{1 \cdot 1821}{675500} \cdot RMultipled fractionsTo multiply two fractions we need to multiply numberators and denominators from first and second fractions: abcd=acbd\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}
7Show source11821 R675500\frac{1 \cdot 1821~R}{675500}Multiply by oneAny number multiplied by one (1) gives the same number: a1=1a=aa \cdot 1 = 1 \cdot a = a
8Show source1821 R675500\frac{1821~R}{675500}Rearrange coefficientsMultiplication and addition are commutative. Due to this property, we can change arguments order to get better readability of expression.
9Show source1821675500 R\frac{1821}{675500}~RResultYour expression reduced to the simplest form known to us.
Numerical result step by step
1Show source18216755008.3144598485\frac{1821}{675500} \cdot 8.3144598485Multipled fractionsTo multiply two fractions we need to multiply numberators and denominators from first and second fractions: abcd=acbd\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}
2Show source18218.3144598485675500\frac{1821 \cdot 8.3144598485}{675500}Simplify arithmetic-
3Show source15140.6313841185675500\frac{15140.6313841185}{675500}Divided fraction-
4Show source0.022413962078635825314581791265729089563286454478164322723908216140.02241396207863582531458179126572908956328645447816432272390821614ResultYour expression reduced to the simplest form known to us.
Units normalization
Show source0.02241396207863582531458179126572908956328645447816432272390821614 [m3] = 22.41396207863582531458179126572908956328645447816432272390821614 [dm3]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=nRTpV = 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:
      p1Vp \propto \dfrac{1}{V}
    • the Charles law - the volume of gas is directly proportional to the temperature:
      VTV \propto T
    • the Avogadro law - the volume of gas is directly proportional to the number of moles of gas in the vessel:
      VnV \propto n
    • the Gay-Lussac law - the gas pressure is directly proportional to the temperature:
      pTp \propto T

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