Function STATE-TEMPERATURE

• Defined in theory: Thermal-system
• Source code: thermal-system.ol

Slots on this function:

Documentation:

the temperature of the dead state

Instance-Of: Function, Quantity-function

Arity: 2

Range: Everywhere-continuous-quantity

Other Related Axioms:

(Forall 
    (?Self ?Time)
    (=> (Active ?Time Non-Steady-State-Flow-Process ?Self)
        (And (Forall (?Cv)
                     (=> (Process-Cv ?Self ?Cv)
                         (= (- (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Heat-Rate ?Self)
                                                     ?T)))
                               (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Work-Rate ?Self)
                                                     ?T))))
                            (+ (- (Lambda 
                                      (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Enthalpy-Rate-Out ?Cv)
                                              ?T)))
                                  (Lambda 
                                      (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Enthalpy-Rate-In ?Cv)
                                              ?T))))
                               (- (Lambda (?T)
                                          (If (= ?T ?Time)
                                              (Value-At 
                                                  (Pe-Rate-Out ?Cv)
                                                  ?T)))
                                  (Lambda (?T)
                                          (If (= ?T ?Time)
                                              (Value-At (Pe-Rate-In ?Cv)
                                                        ?T))))
                               (- (Lambda (?T)
                                          (If (= ?T ?Time)
                                              (Value-At 
                                                  (Ke-Rate-Out ?Cv)
                                                  ?T)))
                                  (Lambda (?T)
                                          (If (= ?T ?Time)
                                              (Value-At (Ke-Rate-In ?Cv)
                                                        ?T))))
                               (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Energy-Rate ?Cv)
                                                     ?T)))))))
             (Forall 
                 (?Cv)
                 (=> (Process-Cv ?Self ?Cv)
                     (= (Lambda (?T)
                                (If (= ?T ?Time)
                                    (Value-At (Energy-Rate ?Cv) ?T)))
                        (+ (Lambda 
                               (?T)
                               (If (= ?T ?Time)
                                   (Value-At (Internal-Energy-Rate ?Cv)
                                             ?T)))
                           (Lambda (?T)
                                   (If (= ?T ?Time)
                                       (Value-At (Ke-Rate ?Cv) ?T)))
                           (Lambda (?T)
                                   (If (= ?T ?Time)
                                       (Value-At (Pe-Rate ?Cv) ?T)))))))
             (Forall 
                 (?Cv)
                 (=> (Process-Cv ?Self ?Cv)
                     (= (Lambda 
                            (?T)
                            (If (= ?T ?Time)
                                (Value-At 
                                    (Entropy-Generation-Rate ?Self)
                                    ?T)))
                        (+ (- (Lambda (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Entropy-Rate-Out ?Cv)
                                              ?T)))
                              (Lambda (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Entropy-Rate-In ?Cv)
                                              ?T))))
                           (- (/ (Lambda (?T)
                                         (If (= ?T ?Time)
                                             (Value-At (Heat-Rate ?Self)
                                                       ?T)))
                                 (Lambda 
                                     (?T)
                                     (If (= ?T ?Time)
                                         (Value-At 
                                             (Heat-Transfer-Temperature ?Self)
                                             ?T)))))
                           (Lambda (?T)
                                   (If (= ?T ?Time)
                                       (Value-At (Entropy-Rate ?Cv)
                                                 ?T)))))))
             (= (Lambda (?T)
                        (If (= ?T ?Time)
                            (Value-At (Irreversibility-Rate ?Self)
                                      ?T)))
                (* (Lambda (?T)
                           (If (= ?T ?Time)
                               (Value-At (Entropy-Generation-Rate ?Self)
                                         ?T)))
                   (Lambda (?T)
                           (If (= ?T ?Time)
                               (Value-At 
                                   (State-Temperature *Dead-State*)
                                   ?T)))))
             (Forall (?Cv)
                     (=> (Process-Cv ?Self ?Cv)
                         (= (Lambda (?T)
                                    (If (= ?T ?Time)
                                        (Value-At (Mass-Rate ?Cv) ?T)))
                            (- (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Mass-Rate-In ?Cv)
                                                     ?T)))
                               (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Mass-Rate-Out ?Cv)
                                                     ?T))))))))))

(Inherited-Facet-Value Slot-Documentation
                       *Dead-State*
                       State-Temperature
                       The Temperature Of The Dead State)

(Quantity.Dimension (State-Temperature ?Self) Temperature-Dimension)

(Inherited-Facet-Value Slot-Cardinality
                       *Dead-State*
                       State-Temperature
                       1)

(Has-Quantity-Function *Dead-State* State-Temperature)

(Slot-Documentation *Dead-State*
                    State-Temperature
                    The Temperature Of The Dead State)

(=> (*Dead-State* ?Self)
    (And (Value-Cardinality ?Self State-Temperature 1)
         (Quantity.Dimension (State-Temperature ?Self)
                             Temperature-Dimension)
         (Value-Cardinality ?Self State-Pressure 1)
         (Quantity.Dimension (State-Pressure ?Self)
                             Pressure-Dimension)
         (Value-Cardinality ?Self State-Entropy 1)
         (Quantity.Dimension (State-Entropy ?Self) Entropy-Dimension)))

(=> (State-Temperature $X $Y) (Everywhere-Continuous-Quantity $Y))