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

abstract:
reference: https://hj.hi.is/EE2/HD1lausn.pdf

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.			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.			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}.	3464107376 $\alpha = \frac{1}{V} \left( \frac{\partial V}{\partial T} \right)_p$ 3497828859 $V = \frac{n R T}{P}$		1311403394 $\alpha = \frac{1}{V} \frac{nR}{P} \left( \frac{\partial T}{\partial T} \right)_P$	LHS diff is -pdg0004686 + pdg0007586 RHS diff is pdg0002834pdg0008179(pdg0007343pdg0007586 - 1)/(pdg0007586pdg0008134)
4	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	1311403394 $\alpha = \frac{1}{V} \frac{nR}{P} \left( \frac{\partial T}{\partial T} \right)_P$		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.			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}.	8435841627 $P V = n R T$	7924842770 $T$	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}.	5962145508 $\alpha = \frac{nR}{VP}$ 2613006036 $\frac{PV}{T} = nR$		6925244346 $\alpha = \frac{PV}{T} \frac{1}{VP}$	LHS diff is -pdg0004686 + pdg0007586pdg0008134/pdg0007343 RHS diff is pdg0002834pdg0008179 - pdg0007586*pdg0008134/pdg0007343
8	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	6925244346 $\alpha = \frac{PV}{T} \frac{1}{VP}$		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.	2472653783 $\alpha = \frac{1}{T}$			no validation is available for declarations

Symbols used in coefficient of thermal expansion using the equation of state for an ideal gas

0000004686: $ \alpha $
0000002834: $ n $
0000008134: $ P $
0000008179: $ R $
0000007343: $ T $
0000007586: $ V $

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timing of Neo4j queries:

0.012 seconds for pdg_app/to_review_derivation e993df96-c5ed-4069-820c-6e736efc29e2
0.007 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivationb5629e70-72e1-4c50-8b7c-f615d2f0f9b7
0.003 seconds for compute/input_feed_output_infrule_for_step: get_inference_rule_connected_to_step_IDb5629e70-72e1-4c50-8b7c-f615d2f0f9b7
0.003 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type HAS_INPUTb5629e70-72e1-4c50-8b7c-f615d2f0f9b7
0.002 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_FEEDb5629e70-72e1-4c50-8b7c-f615d2f0f9b7
0.002 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_OUTPUTb5629e70-72e1-4c50-8b7c-f615d2f0f9b7
0.002 seconds for compute/get_dict_of_steps_in_derivation: get_sequence_index_for_stepb5629e70-72e1-4c50-8b7c-f615d2f0f9b7
0.004 seconds for pdg_app/ e993df96-c5ed-4069-820c-6e736efc29e2

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.			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.			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}.	3464107376 \(\alpha = \frac{1}{V} \left( \frac{\partial V}{\partial T} \right)_p\) 3497828859 \(V = \frac{n R T}{P}\)		1311403394 \(\alpha = \frac{1}{V} \frac{nR}{P} \left( \frac{\partial T}{\partial T} \right)_P\)	LHS diff is -pdg0004686 + pdg0007586 RHS diff is pdg0002834pdg0008179(pdg0007343pdg0007586 - 1)/(pdg0007586pdg0008134)
4	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	1311403394 \(\alpha = \frac{1}{V} \frac{nR}{P} \left( \frac{\partial T}{\partial T} \right)_P\)		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.			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}.	8435841627 \(P V = n R T\)	7924842770 \(T\)	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}.	5962145508 \(\alpha = \frac{nR}{VP}\) 2613006036 \(\frac{PV}{T} = nR\)		6925244346 \(\alpha = \frac{PV}{T} \frac{1}{VP}\)	LHS diff is -pdg0004686 + pdg0007586pdg0008134/pdg0007343 RHS diff is pdg0002834pdg0008179 - pdg0007586*pdg0008134/pdg0007343
8	0000111457: simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\ref{eq:#1}; yields Eq.~\ref{eq:#2}.	6925244346 \(\alpha = \frac{PV}{T} \frac{1}{VP}\)		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.	2472653783 \(\alpha = \frac{1}{T}\)			no validation is available for declarations