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Review coefficient of thermal expansion using the equation of state for an ideal gas

step inference rule input feed output step validity (as per SymPy)
1
  • 0000111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an initial equation.
  1. 3464107376
    \(\alpha = \frac{1}{V} \left( \frac{\partial V}{\partial T} \right)_p\)
 no validation is available for declarations
2
  • 0000111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an initial equation.
  1. 3497828859
    \(V = \frac{n R T}{P}\)
 no validation is available for declarations
3
  • 0000111556: substitute LHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute LHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.
  1. 3464107376
    \(\alpha = \frac{1}{V} \left( \frac{\partial V}{\partial T} \right)_p\)
  1. 3497828859
    \(V = \frac{n R T}{P}\)
  1. 1311403394
    \(\alpha = \frac{1}{V} \frac{nR}{P} \left( \frac{\partial T}{\partial T} \right)_P\)
 LHS diff is -pdg0004686 + pdg0007586 RHS diff is pdg0002834*pdg0008179*(pdg0007343*pdg0007586 - 1)/(pdg0007586*pdg0008134)
4
  • 0000111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.
  1. 1311403394
    \(\alpha = \frac{1}{V} \frac{nR}{P} \left( \frac{\partial T}{\partial T} \right)_P\)
  1. 5962145508
    \(\alpha = \frac{nR}{VP}\)
 valid
5
  • 0000111981: declare initial expression
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\ref{eq:#1} is an initial equation.
  1. 8435841627
    \(P V = n R T\)
 no validation is available for declarations
6
  • 0000111975: divide both sides by
  • number of inputs: 1; feeds: 1; outputs: 1
  • Divide both sides of Eq.~\ref{eq:#2} by $#1$; yields Eq.~\ref{eq:#3}.
  1. 8435841627
    \(P V = n R T\)
  1. 7924842770
    \(T\)
  1. 2613006036
    \(\frac{PV}{T} = nR\)
 valid
7
  • 0000111634: substitute RHS of expr 1 into expr 2
  • number of inputs: 2; feeds: 0; outputs: 1
  • Substitute RHS of Eq.~\ref{eq:#1} into Eq.~\ref{eq:#2}; yields Eq.~\ref{eq:#3}.
  1. 5962145508
    \(\alpha = \frac{nR}{VP}\)
  1. 2613006036
    \(\frac{PV}{T} = nR\)
  1. 6925244346
    \(\alpha = \frac{PV}{T} \frac{1}{VP}\)
 LHS diff is -pdg0004686 + pdg0007586*pdg0008134/pdg0007343 RHS diff is pdg0002834*pdg0008179 - pdg0007586*pdg0008134/pdg0007343
8
  • 0000111457: simplify
  • number of inputs: 1; feeds: 0; outputs: 1
  • Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.
  1. 6925244346
    \(\alpha = \frac{PV}{T} \frac{1}{VP}\)
  1. 2472653783
    \(\alpha = \frac{1}{T}\)
 LHS diff is 0 RHS diff is (pdg0007586*pdg0008134 - 1)/pdg0007343
9
  • 0000111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\ref{eq:#1} is one of the final equations.
  1. 2472653783
    \(\alpha = \frac{1}{T}\)
 no validation is available for declarations

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