ThermodynamicData
Entity
EntityProperty
Quantity
UnitConvert
ListLinePlot
NIntegrate
Interpolation

Engineering
Physics
Chemistry

Stirling Cycle with Real-World Materials

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Explore the properties of a Stirling cycle, from expansion curves to efficiency

Examine the Stirling cycle for 10 moles of air:

In[1]:=

mAir=

mol

dry air

CHEMICAL



molar mass



Out[1]=

289.6

Use

ThermodynamicData

to calculate the isothermal expansion and compression curves at 200 °C and 120 °C, respectively:

In[2]:=

isothermalExpansion=Transpose[Values[ThermodynamicData["Air",{"SpecificVolume","Pressure"},{"Temperature"Quantity[200,"DegreesCelcius"],"Pressure"Quantity[Range[100,200]1000,"Pascals"]}]]*{mAir,1}];

In[3]:=

isothermalCompression=Transpose[Values[ThermodynamicData["Air",{"SpecificVolume","Pressure"},{"Temperature"Quantity[120,"DegreesCelcius"],"Pressure"Quantity[Range[100,200]1000,"Pascals"]}]]*{mAir,1}];

Create the pressure–volume (PV) diagram:

In[4]:=

ListLinePlot{isothermalExpansion,isothermalCompression},



Out[4]=

Calculate mechanical work through

∫

P(V)V

with V ranging from 0.2 to 0.3:

In[5]:=

W=Quantity[NIntegrate[Evaluate[Interpolation[QuantityMagnitude[isothermalExpansion]][V]-Interpolation[QuantityMagnitude[isothermalCompression]][V]],{V,0.2,0.3}],"Joules"]

Out[5]=

2701.38

Find maximal and minimal pressures for expansion and compression:

In[6]:=

{pMax1,pMin1}=Quantity[Interpolation[QuantityMagnitude[isothermalExpansion]][{0.2,0.3}],"Pascals"]

Out[6]=

{

196781.

131161.

}

In[7]:=

{pMax2,pMin2}=Quantity[Interpolation[QuantityMagnitude[isothermalCompression]][{0.2,0.3}],"Pascals"]

Out[7]=

{

163456.

108961.

}

Calculate the change in internal energy:

In[8]:=

U[T_,p_]:=ThermodynamicData["Air","InternalEnergy",{"Temperature"T,"Pressure"p}]*mAir;ΔU=U[Quantity[200,"DegreesCelcius"],pMax1]-U[Quantity[120,"DegreesCelcius"],pMin2]

Out[8]=

16919.

Using work and the change in internal energy, calculate efficiency:

In[9]:=

ΔU

Out[9]=

0.159666

Compare with maximal possible (Carnot) efficiency:

In[10]:=

1.-

UnitConvert[Quantity[120,"DegreesCelcius"],"Kelvins"]

UnitConvert[Quantity[200,"DegreesCelcius"],"Kelvins"]

Out[10]=

0.16908

Related Symbols

ThermodynamicData
Entity
EntityProperty
Quantity
UnitConvert
ListLinePlot
NIntegrate
Interpolation

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Contributed by: Wolfram Staff