Function WORK-RATE


Slots on this function:

Documentation:
the rate at which energy is trasferred out across the system boundary by work
Instance-Of: Function, Quantity-function
Arity: 2
Range: Everywhere-continuous-quantity

Other Related Axioms:

(Forall 
    (?Self ?Time)
    (=> (Active ?Time Cycle-Work-Output ?Self)
        (C+ (Lambda (?T)
                    (If (= ?T ?Time)
                        (Value-At (Work-Rate (Process-Involved ?Self))
                                  ?T)))
            (Lambda 
                (?T)
                (If (= ?T ?Time)
                    (Value-At 
                        (Net-Work-Output-Rate (Cycle-Involved ?Self))
                        ?T))))))

(Inherited-Facet-Value 
    Slot-Documentation
    Thermal-Process
    Work-Rate
    The Rate At Which  Energy Is Trasferred Out Across The System Boundary By Work)

(Quantity.Dimension (Work-Rate ?Self) Power-Dimension)

(Inherited-Facet-Value Slot-Cardinality Thermal-Process Work-Rate 1)

(Has-Quantity-Function Thermal-Process Work-Rate)

(Slot-Documentation 
    Thermal-Process
    Work-Rate
    The Rate At Which  Energy Is Trasferred Out Across The System Boundary By Work)

(=> (Thermal-Process ?Self)
    (And (Value-Cardinality ?Self Work-Rate 1)
         (Quantity.Dimension (Work-Rate ?Self) Power-Dimension)
         (Value-Cardinality ?Self Heat-Rate 1)
         (Quantity.Dimension (Heat-Rate ?Self) Power-Dimension)
         (Value-Cardinality ?Self Heat-Transfer-Temperature 1)
         (Quantity.Dimension (Heat-Transfer-Temperature ?Self)
                             Temperature-Dimension)
         (Value-Cardinality ?Self Entropy-Generation-Rate 1)
         (Quantity.Dimension (Entropy-Generation-Rate ?Self)
                             Entropy-Rate-Dimension)
         (Value-Cardinality ?Self Irreversibility-Rate 1)
         (Quantity.Dimension (Irreversibility-Rate ?Self)
                             Power-Dimension)
         (Value-Cardinality ?Self Internally-Reversible-P 1)))

(=> (Work-Rate $X $Y) (Everywhere-Continuous-Quantity $Y))

(Forall 
    (?Self ?Time)
    (=> (Active ?Time Steady-State-Steady-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 (D-Pe-Rate ?Cv)
                                                     ?T)))
                               (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (D-Ke-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)))))))))
             (Forall (?Cv)
                     (=> (Process-Cv ?Self ?Cv)
                         (= (Lambda (?T)
                                    (If (= ?T ?Time)
                                        (Value-At (Mass-Rate-In ?Cv)
                                                  ?T)))
                            (Lambda (?T)
                                    (If (= ?T ?Time)
                                        (Value-At (Mass-Rate-Out ?Cv)
                                                  ?T)))))))))

(Forall (?Self ?Time)
        (=> (Active ?Time Steady-Flow-Adiabatic-Heat-Exchange ?Self)
            (And (= (Lambda (?T)
                            (If (= ?T ?Time)
                                (Value-At (Work-Rate ?Self) ?T)))
                    0)
                 (Forall (?Cv)
                         (=> (Process-Cv ?Self ?Cv)
                             (= (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (D-Ke-Rate ?Cv)
                                                      ?T)))
                                0)))
                 (Forall (?Cv)
                         (=> (Process-Cv ?Self ?Cv)
                             (= (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (D-Pe-Rate ?Cv)
                                                      ?T)))
                                0))))))

(Forall (?Self ?Time)
        (=> (Active ?Time Steady-Flow-Heat-Transfer ?Self)
            (And (= (Lambda (?T)
                            (If (= ?T ?Time)
                                (Value-At (Work-Rate ?Self) ?T)))
                    0)
                 (Forall (?Cv)
                         (=> (Process-Cv ?Self ?Cv)
                             (= (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (D-Ke-Rate ?Cv)
                                                      ?T)))
                                0)))
                 (Forall (?Cv)
                         (=> (Process-Cv ?Self ?Cv)
                             (= (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (D-Pe-Rate ?Cv)
                                                      ?T)))
                                0))))))

(Forall (?Self ?Time)
        (=> (Active ?Time Steady-Flow-Throttling ?Self)
            (And (= (Lambda (?T)
                            (If (= ?T ?Time)
                                (Value-At (Work-Rate ?Self) ?T)))
                    0)
                 (Forall (?Cv)
                         (=> (Process-Cv ?Self ?Cv)
                             (= (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Pe-Rate-Out ?Cv)
                                                      ?T)))
                                (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Pe-Rate-In ?Cv)
                                                      ?T))))))
                 (Forall (?Cv)
                         (=> (Process-Cv ?Self ?Cv)
                             (= (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Ke-Rate-Out ?Cv)
                                                      ?T)))
                                (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Ke-Rate-In ?Cv)
                                                      ?T)))))))))

(Forall (?Self ?Time)
        (=> (Active ?Time Steady-Flow-Adiabatic-Mixing ?Self)
            (And (= (Lambda (?T)
                            (If (= ?T ?Time)
                                (Value-At (Work-Rate ?Self) ?T)))
                    0)
                 (Forall (?Cv)
                         (=> (Process-Cv ?Self ?Cv)
                             (= (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Ke-Rate-Out ?Cv)
                                                      ?T)))
                                (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Ke-Rate-In ?Cv)
                                                      ?T))))))
                 (Forall (?Cv)
                         (=> (Process-Cv ?Self ?Cv)
                             (= (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Pe-Rate-Out ?Cv)
                                                      ?T)))
                                (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Pe-Rate-In ?Cv)
                                                      ?T)))))))))

(Forall (?Self ?Time)
        (=> (Active ?Time Steady-Flow-In-Nozzle ?Self)
            (And (= (Lambda (?T)
                            (If (= ?T ?Time)
                                (Value-At (Work-Rate ?Self) ?T)))
                    0)
                 (Forall (?Cv)
                         (=> (Process-Cv ?Self ?Cv)
                             (= (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Pe-Rate-Out ?Cv)
                                                      ?T)))
                                (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Pe-Rate-In ?Cv)
                                                      ?T)))))))))

(Forall (?Self ?Time)
        (=> (Active ?Time Steady-Flow-In-Diffuser ?Self)
            (And (= (Lambda (?T)
                            (If (= ?T ?Time)
                                (Value-At (Work-Rate ?Self) ?T)))
                    0)
                 (Forall (?Cv)
                         (=> (Process-Cv ?Self ?Cv)
                             (= (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Pe-Rate-Out ?Cv)
                                                      ?T)))
                                (Lambda (?T)
                                        (If (= ?T ?Time)
                                            (Value-At (Pe-Rate-In ?Cv)
                                                      ?T)))))))))

(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))))))))))