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Ciencias Básicas de Ingeniería - Un Enfoque de Sistemas, Contabilidad y Modelado (Richards)
9: Apéndices
9.3: Apéndice C- Resumen de Ecuaciones de Conservación y Contabilidad, Conversiones de Unidades, Modelos de Propiedades, Datos de Propiedades Termofísicas

9.3: Apéndice C- Resumen de Ecuaciones de Conservación y Contabilidad, Conversiones de Unidades, Modelos de Propiedades, Datos de Propiedades Termofísicas

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C.1: Ecuaciones Básicas de Conservación y Contabilidad

Ecuaciones Básicas de Conservación y Contabilidad
Ecuación contable para la propiedad genérica y extensa\(B\) : Propiedad Extensa —\(\displaystyle B_{sys} (t) = \iiint\limits_{V_{sys}} b_{(x, y, z, t)} \rho_{(x, y, z, t)} dV\) Ecuación Contable —\(\dfrac{dB_{sys} (t)}{dt} = \dot{B}_{in} - \dot{B}_{out} + \dot{B}_{gen} - \dot{B}_{cons}\) \[\underbrace{\frac{d B_{sys}}{d t}}_{\text {Accumulation}} = \underbrace{ \underbrace{\left\{\dot{B}_{in}-\dot{B}_{out}\right\}}_{\text {non-flow boundaries}} + \underbrace{\left\{\sum_{in} \dot{m}_{i} b_{i}-\sum_{out} \dot{m}_{e} b_{e}\right\}}_{\text {flow boundaries}} }_{\text {Transport}} + \underbrace{\left\{\dot{B}_{\text {gen}} - \dot{B}_{\text {cons}}\right\}}_{\text {Generation/Consumption}} \nonumber \]	Conservación del Momentum Lineal:\(\displaystyle \quad \mathbf{P}_{sys} = \int\limits_{V_{sys}} \mathbf{V} \rho \ dV\) \[\frac{d \mathbf{P}_{sys}}{dt} = \sum_{j} \mathbf{F}_{\text{ext, } j} + \left\{\sum_{in} \dot{m}_{i} \mathbf{V}_{i} - \sum_{out} \dot{m}_{e} \mathbf{V}_{e} \right\} \nonumber \]
Conservación de la Masa:\(\displaystyle \quad m_{sys} (t)=\iiint\limits_{V_{sys}} \rho_{(x, y, z, t)} \ d V\) \[\frac{d m_{sys}}{dt} = \sum_{in} \dot{m}_{i} - \sum_{out} \dot{m}_{e} \nonumber \] \[\text{where } \dot{m} = \int\limits_{A_C} \rho V_{n} \ dA_{C} = \underbrace{\rho A_{C} V_{\text{avg}}}_{\text{1-D Flow Assumption}} \quad \text{(the mass flow rate)} \nonumber \]	Conservación del Momentum Angular:\(\displaystyle \quad \mathbf{L}_{o, \ sys} = \int\limits_{V_{sys}} (\mathbf{r} \times \mathbf{V}) \rho \ dV\) \[\frac{d \mathbf{L}_{o, \ sys}}{dt} = \sum_{j} \mathbf{M}_{o, \ j} + \left\{\sum_{in} \dot{m}_{i} \left(\mathbf{r}_{i} \times \mathbf{V}_{i}\right) -\sum_{out} \dot{m}_{e} \left(\mathbf{r}_{e} \times \mathbf{V}_{e} \right)\right\} \nonumber \] \[\text{where } \mathbf{M}_{o, j} = \mathbf{r}_{j} \times \mathbf{F}_{j} \quad \text{or} \quad M_{\text{couple, } j} \nonumber \]
Contabilidad de Especies Químicas:\(\quad m_{j}=n_{j} M_{j}\) \[\text{mass} \quad \rightarrow \quad \frac{d m_{j, \ sys}}{d t} = \sum_{in} \dot{m}_{j, i} - \sum_{out} \dot{m}_{j, e} + \left(\dot{m}_{j, \ gen}-\dot{m}_{j, \ cons}\right) \nonumber \] \[ \text{molar} \quad \rightarrow \quad \frac{d n_{j, \ sys}}{dt} = \sum_{in} \dot{n}_{j, \ i} - \sum_{out} \dot{n}_{j, \ e} + \left( \dot{n}_{j, \ gen} - \dot{n}_{j, \ cons} \right) \nonumber \]	Conservación de la Energía: \[\begin{gathered} E_{sys} = \int\limits_{V_{sys}} e \rho \ dV \quad \text { where } \quad e = u+\frac{V^{2}}{2}+gz+e_{\text {spring}} + \ldots \\ \frac{dE_{sys}}{dt} = \dot{Q}_{\text{net, in}} + \dot{W}_{\text {net, in}} + \left\{ \sum_{in} \dot{m}_{i} \left(h_{i} + \frac{V_{i}^{2}}{2} + gz_{i} \right) - \sum_{out} \dot{m}_{e} \left(h_{e} + \frac{V_{e}^{2}}{2} + gz_{e}\right) \right\} \end{gathered} \nonumber \]
Conservación de Carga:\(\displaystyle \quad q_{sys} = \int\limits_{V_{sys}} \tilde{q} \rho \ dV\) \[\frac{d q_{sys}}{dt} = \sum_{in} \dot{q}_{i} - \sum_{out} \dot{q}_{e} \nonumber \]	Contabilidad de Entropía:\(\displaystyle \quad S_{sys} = \int\limits_{V_{sys}} s \rho \ dV \quad \text{and} \quad S_{gen} \geq 0\) \[\frac{d S_{sys}}{dt} = \sum_{j} \frac{\dot{Q}_{j}}{T_{b, \ j}} + \left\{ \sum_{in} \dot{m}_{i} s_{i} - \sum_{out} \dot{m}_{e} s_{e}\right\} + \dot{S}_{gen} \nonumber \]

Ecuaciones Básicas de Conservación y Contabilidad

Ecuación contable para la propiedad genérica y extensa\(B\) :

Propiedad Extensa —\(\displaystyle B_{sys} (t) = \iiint\limits_{V_{sys}} b_{(x, y, z, t)} \rho_{(x, y, z, t)} dV\)

Ecuación Contable —\(\dfrac{dB_{sys} (t)}{dt} = \dot{B}_{in} - \dot{B}_{out} + \dot{B}_{gen} - \dot{B}_{cons}\)

\[\underbrace{\frac{d B_{sys}}{d t}}_{\text {Accumulation}} = \underbrace{ \underbrace{\left\{\dot{B}_{in}-\dot{B}_{out}\right\}}_{\text {non-flow boundaries}} + \underbrace{\left\{\sum_{in} \dot{m}_{i} b_{i}-\sum_{out} \dot{m}_{e} b_{e}\right\}}_{\text {flow boundaries}} }_{\text {Transport}} + \underbrace{\left\{\dot{B}_{\text {gen}} - \dot{B}_{\text {cons}}\right\}}_{\text {Generation/Consumption}} \nonumber \]

Conservación del Momentum Lineal:\(\displaystyle \quad \mathbf{P}_{sys} = \int\limits_{V_{sys}} \mathbf{V} \rho \ dV\)

\[\frac{d \mathbf{P}_{sys}}{dt} = \sum_{j} \mathbf{F}_{\text{ext, } j} + \left\{\sum_{in} \dot{m}_{i} \mathbf{V}_{i} - \sum_{out} \dot{m}_{e} \mathbf{V}_{e} \right\} \nonumber \]

Conservación de la Masa:\(\displaystyle \quad m_{sys} (t)=\iiint\limits_{V_{sys}} \rho_{(x, y, z, t)} \ d V\)

\[\frac{d m_{sys}}{dt} = \sum_{in} \dot{m}_{i} - \sum_{out} \dot{m}_{e} \nonumber \]

\[\text{where } \dot{m} = \int\limits_{A_C} \rho V_{n} \ dA_{C} = \underbrace{\rho A_{C} V_{\text{avg}}}_{\text{1-D Flow Assumption}} \quad \text{(the mass flow rate)} \nonumber \]

Conservación del Momentum Angular:\(\displaystyle \quad \mathbf{L}_{o, \ sys} = \int\limits_{V_{sys}} (\mathbf{r} \times \mathbf{V}) \rho \ dV\)

\[\frac{d \mathbf{L}_{o, \ sys}}{dt} = \sum_{j} \mathbf{M}_{o, \ j} + \left\{\sum_{in} \dot{m}_{i} \left(\mathbf{r}_{i} \times \mathbf{V}_{i}\right) -\sum_{out} \dot{m}_{e} \left(\mathbf{r}_{e} \times \mathbf{V}_{e} \right)\right\} \nonumber \]

\[\text{where } \mathbf{M}_{o, j} = \mathbf{r}_{j} \times \mathbf{F}_{j} \quad \text{or} \quad M_{\text{couple, } j} \nonumber \]

Contabilidad de Especies Químicas:\(\quad m_{j}=n_{j} M_{j}\)

\[\text{mass} \quad \rightarrow \quad \frac{d m_{j, \ sys}}{d t} = \sum_{in} \dot{m}_{j, i} - \sum_{out} \dot{m}_{j, e} + \left(\dot{m}_{j, \ gen}-\dot{m}_{j, \ cons}\right) \nonumber \]

\[ \text{molar} \quad \rightarrow \quad \frac{d n_{j, \ sys}}{dt} = \sum_{in} \dot{n}_{j, \ i} - \sum_{out} \dot{n}_{j, \ e} + \left( \dot{n}_{j, \ gen} - \dot{n}_{j, \ cons} \right) \nonumber \]

Conservación de la Energía:

\[\begin{gathered} E_{sys} = \int\limits_{V_{sys}} e \rho \ dV \quad \text { where } \quad e = u+\frac{V^{2}}{2}+gz+e_{\text {spring}} + \ldots \\ \frac{dE_{sys}}{dt} = \dot{Q}_{\text{net, in}} + \dot{W}_{\text {net, in}} + \left\{ \sum_{in} \dot{m}_{i} \left(h_{i} + \frac{V_{i}^{2}}{2} + gz_{i} \right) - \sum_{out} \dot{m}_{e} \left(h_{e} + \frac{V_{e}^{2}}{2} + gz_{e}\right) \right\} \end{gathered} \nonumber \]

Conservación de Carga:\(\displaystyle \quad q_{sys} = \int\limits_{V_{sys}} \tilde{q} \rho \ dV\)

\[\frac{d q_{sys}}{dt} = \sum_{in} \dot{q}_{i} - \sum_{out} \dot{q}_{e} \nonumber \]

Contabilidad de Entropía:\(\displaystyle \quad S_{sys} = \int\limits_{V_{sys}} s \rho \ dV \quad \text{and} \quad S_{gen} \geq 0\)

\[\frac{d S_{sys}}{dt} = \sum_{j} \frac{\dot{Q}_{j}}{T_{b, \ j}} + \left\{ \sum_{in} \dot{m}_{i} s_{i} - \sum_{out} \dot{m}_{e} s_{e}\right\} + \dot{S}_{gen} \nonumber \]

C.2 Conversiones de Unidades

Conversiones de unidades
Largo \[\begin{aligned} & 1 \mathrm{~ft} = 12 \mathrm{~in} = 0.3048 \mathrm{~m} = 1/3 \mathrm{~yd} \\ & 1 \mathrm{~m} = 100 \mathrm{~cm} = 1000 \mathrm{~mm} = 39.37 \mathrm{~in} = 3.2808 \mathrm{~ft} \\ & 1 \mathrm{~mile} = 5280 \mathrm{~ft} = 1609.3 \mathrm{~m} \end{aligned} \nonumber \]	Fuerza \[\begin{aligned} & 1 \mathrm{~N} = 1 \mathrm{~kg} \cdot \mathrm{m}/\mathrm{s}^{2} = 0.22481 \mathrm{~lbf} \\ & 1 \mathrm{~lbf} = 1 \mathrm{~slug} \cdot \mathrm{ft}/\mathrm{s}^{2} = 32.174 \mathrm{~lbm} \cdot \mathrm{ft}/\mathrm{s}^{2} = 4.4482 \mathrm{~N} \end{aligned} \nonumber \]
Masa \[\begin{aligned} &1 \mathrm{~kg} = 1000 \mathrm{~g} = 2.2046 \mathrm{~lbm} \\ &1 \mathrm{~lbm} = 16 \mathrm{~oz} = 0.45359 \mathrm{~kg} \\ &1 \mathrm{~slug} = 32.174 \mathrm{~lbm} \end{aligned} \nonumber \]	Presión \[\begin{aligned} & 1 \mathrm{~atm} = 101.325 \mathrm{~kPa} = 1.01325 \mathrm{~bar} = 14.696 \mathrm{~lbf}/\mathrm{in}^{2} \\ & 1 \mathrm{~bar} = 100 \mathrm{~kPa} = 10^{5} \mathrm{~Pa} \\ & 1 \mathrm{~Pa} = 1 \mathrm{~N}/\mathrm{m}^{2} = 10^{-3} \mathrm{~kPa} \\ & 1 \mathrm{~lbf}/\mathrm{in}^{2} = 6.8947 \mathrm{~kPa} = 6894.7 \mathrm{~N}/\mathrm{m}^{2} \\ & \quad \left[ \mathrm{lbf}/\mathrm{in}^{2} \text{ often abbreviated as “psi”} \right] \end{aligned} \nonumber \]
Valores de temperatura \[\begin{aligned} & (\mathrm{T} / \mathrm{K}) = \left(\mathrm{T} / { }^{\circ} \mathrm{R}\right) / 1.8 \\ & (\mathrm{T} / \mathrm{K}) = \left(\mathrm{T} / { }^{\circ} \mathrm{C} \right) + 273.15 \\ & \left(\mathrm{T} / { }^{\circ} \mathrm{C} \right) = \left[ \left( \mathrm{T} /{ }^{\circ} \mathrm{F} \right) - 32 \right]/1.8 \\ & \left(\mathrm{T} / \mathrm{R} \right) = 1.8 (\mathrm{T}/\mathrm{K}) \\ & \left( \mathrm{T}/{ }^{\circ} \mathrm{R}\right) = \left( \mathrm{T}/{ }^{\circ} \mathrm{F} \right) + 459.67 \\ & \left( \mathrm{T}/{ }^{\circ} \mathrm{F} \right) = 1.8 \left( \mathrm{T}/{ }^{\circ} \mathrm{C}\right) + 32 \end{aligned} \nonumber \]	Energía \[\begin{aligned} & 1 \mathrm{~J} = 1 \mathrm{~N} \cdot \mathrm{m} \\ & 1 \mathrm{~kJ} = 1000 \mathrm{~J} = 737.56 \mathrm{~ft} \cdot \mathrm{lbf} = 0.94782 \mathrm{~Btu} \\ & 1 \mathrm{~Btu} = 1.0551 \mathrm{~kJ} = 778.17 \mathrm{~ft} \cdot \mathrm{lbf} \\ & 1 \mathrm{~ft} \cdot \mathrm{lbf} = 1.3558 \mathrm{~J} \end{aligned} \nonumber \]
Diferencias de temperatura \[\begin{aligned} & (\Delta \mathrm{T}/{ }^{\circ} \mathrm{R}) = 1.8 (\Delta \mathrm{T}/\mathrm{K}) \\ & (\Delta \mathrm{T}/{ }^{\circ} \mathrm{R}) = (\Delta \mathrm{T}/{ }^{\circ} \mathrm{F}) \\ & (\Delta \mathrm{T}/\mathrm{K}) = (\Delta \mathrm{T}/{ }^{\circ} \mathrm{C}) \end{aligned} \nonumber \]	Tasa de transferencia de energía \[\begin{aligned} & 1 \mathrm{~kW} = 1 \mathrm{~kJ}/\mathrm{s} = 737.56 \mathrm{~ft} \cdot \mathrm{lbf}/\mathrm{s} = 1.3410 \mathrm{~hp} = 0.94782 \mathrm{~Btu}/\mathrm{s} \\ & 1 \mathrm{~Btu}/\mathrm{s} = 1.0551 \mathrm{~kW} = 1.4149 \mathrm{~hp} = 778.17 \mathrm{~ft} \cdot \mathrm{lbf}/\mathrm{s} \\ & 1 \mathrm{~hp} = 550 \mathrm{~ft} \cdot \mathrm{lbf}/\mathrm{s} = 0.74571 \mathrm{~kW} = 0.70679 \mathrm{~Btu}/\mathrm{s} \end{aligned} \nonumber \]
Volumen \[\begin{aligned} & 1 \mathrm{~m}^{3} = 1000 \mathrm{~L} = 10^{6} \mathrm{~cm}^{3} = 10^{6} \mathrm{~mL} = 35.315 \mathrm{~ft}^{3} = 264.17 \mathrm{~gal} \\ & 1 \mathrm{~ft}^{3} = 1728 \mathrm{~in}^{3} = 7.4805 \mathrm{~gal} = 0.028317 \mathrm{~m}^{3} \\ & 1 \mathrm{~gal} = 0.13368 \mathrm{~ft}^{3} = 0.0037854 \mathrm{~m}^{3} \end{aligned} \nonumber \]	Energía Específica \[\begin{aligned} & 1 \mathrm{~kJ}/\mathrm{kg} = 1000 \mathrm{~m}^{2}/\mathrm{s}^{2} \\ & 1 \mathrm{~Btu}/\mathrm{lbm} = 25037 \mathrm{~ft}^{2}/\mathrm{s}^{2} \\ & 1 \mathrm{~ft} \cdot \mathrm{lbf}/\mathrm{lbm} = 32.174 \mathrm{~ft}^{2}/\mathrm{s}^{2} \end{aligned} \nonumber \]
Caudal Volumétrico \[\begin{aligned} & 1 \mathrm{~m}^{3}/\mathrm{s} = 35.315 \mathrm{~ft}^{3}/\mathrm{s} = 264.17 \mathrm{~gal}/\mathrm{s} \\ & 1 \mathrm{~ft}^{3}/\mathrm{s} = 1.6990 \mathrm{~m}^{3}/\mathrm{min} = 7.4805 \mathrm{~gal}/\mathrm{s} = 448.83 \mathrm{~gal}/\mathrm{~min} \end{aligned} \nonumber \]

Conversiones de unidades

Largo

\[\begin{aligned} & 1 \mathrm{~ft} = 12 \mathrm{~in} = 0.3048 \mathrm{~m} = 1/3 \mathrm{~yd} \\ & 1 \mathrm{~m} = 100 \mathrm{~cm} = 1000 \mathrm{~mm} = 39.37 \mathrm{~in} = 3.2808 \mathrm{~ft} \\ & 1 \mathrm{~mile} = 5280 \mathrm{~ft} = 1609.3 \mathrm{~m} \end{aligned} \nonumber \]

Fuerza

\[\begin{aligned} & 1 \mathrm{~N} = 1 \mathrm{~kg} \cdot \mathrm{m}/\mathrm{s}^{2} = 0.22481 \mathrm{~lbf} \\ & 1 \mathrm{~lbf} = 1 \mathrm{~slug} \cdot \mathrm{ft}/\mathrm{s}^{2} = 32.174 \mathrm{~lbm} \cdot \mathrm{ft}/\mathrm{s}^{2} = 4.4482 \mathrm{~N} \end{aligned} \nonumber \]

Masa

\[\begin{aligned} &1 \mathrm{~kg} = 1000 \mathrm{~g} = 2.2046 \mathrm{~lbm} \\ &1 \mathrm{~lbm} = 16 \mathrm{~oz} = 0.45359 \mathrm{~kg} \\ &1 \mathrm{~slug} = 32.174 \mathrm{~lbm} \end{aligned} \nonumber \]

Presión

\[\begin{aligned} & 1 \mathrm{~atm} = 101.325 \mathrm{~kPa} = 1.01325 \mathrm{~bar} = 14.696 \mathrm{~lbf}/\mathrm{in}^{2} \\ & 1 \mathrm{~bar} = 100 \mathrm{~kPa} = 10^{5} \mathrm{~Pa} \\ & 1 \mathrm{~Pa} = 1 \mathrm{~N}/\mathrm{m}^{2} = 10^{-3} \mathrm{~kPa} \\ & 1 \mathrm{~lbf}/\mathrm{in}^{2} = 6.8947 \mathrm{~kPa} = 6894.7 \mathrm{~N}/\mathrm{m}^{2} \\ & \quad \left[ \mathrm{lbf}/\mathrm{in}^{2} \text{ often abbreviated as “psi”} \right] \end{aligned} \nonumber \]

Valores de temperatura

\[\begin{aligned} & (\mathrm{T} / \mathrm{K}) = \left(\mathrm{T} / { }^{\circ} \mathrm{R}\right) / 1.8 \\ & (\mathrm{T} / \mathrm{K}) = \left(\mathrm{T} / { }^{\circ} \mathrm{C} \right) + 273.15 \\ & \left(\mathrm{T} / { }^{\circ} \mathrm{C} \right) = \left[ \left( \mathrm{T} /{ }^{\circ} \mathrm{F} \right) - 32 \right]/1.8 \\ & \left(\mathrm{T} / \mathrm{R} \right) = 1.8 (\mathrm{T}/\mathrm{K}) \\ & \left( \mathrm{T}/{ }^{\circ} \mathrm{R}\right) = \left( \mathrm{T}/{ }^{\circ} \mathrm{F} \right) + 459.67 \\ & \left( \mathrm{T}/{ }^{\circ} \mathrm{F} \right) = 1.8 \left( \mathrm{T}/{ }^{\circ} \mathrm{C}\right) + 32 \end{aligned} \nonumber \]

Energía

\[\begin{aligned} & 1 \mathrm{~J} = 1 \mathrm{~N} \cdot \mathrm{m} \\ & 1 \mathrm{~kJ} = 1000 \mathrm{~J} = 737.56 \mathrm{~ft} \cdot \mathrm{lbf} = 0.94782 \mathrm{~Btu} \\ & 1 \mathrm{~Btu} = 1.0551 \mathrm{~kJ} = 778.17 \mathrm{~ft} \cdot \mathrm{lbf} \\ & 1 \mathrm{~ft} \cdot \mathrm{lbf} = 1.3558 \mathrm{~J} \end{aligned} \nonumber \]

Diferencias de temperatura

\[\begin{aligned} & (\Delta \mathrm{T}/{ }^{\circ} \mathrm{R}) = 1.8 (\Delta \mathrm{T}/\mathrm{K}) \\ & (\Delta \mathrm{T}/{ }^{\circ} \mathrm{R}) = (\Delta \mathrm{T}/{ }^{\circ} \mathrm{F}) \\ & (\Delta \mathrm{T}/\mathrm{K}) = (\Delta \mathrm{T}/{ }^{\circ} \mathrm{C}) \end{aligned} \nonumber \]

Tasa de transferencia de energía

\[\begin{aligned} & 1 \mathrm{~kW} = 1 \mathrm{~kJ}/\mathrm{s} = 737.56 \mathrm{~ft} \cdot \mathrm{lbf}/\mathrm{s} = 1.3410 \mathrm{~hp} = 0.94782 \mathrm{~Btu}/\mathrm{s} \\ & 1 \mathrm{~Btu}/\mathrm{s} = 1.0551 \mathrm{~kW} = 1.4149 \mathrm{~hp} = 778.17 \mathrm{~ft} \cdot \mathrm{lbf}/\mathrm{s} \\ & 1 \mathrm{~hp} = 550 \mathrm{~ft} \cdot \mathrm{lbf}/\mathrm{s} = 0.74571 \mathrm{~kW} = 0.70679 \mathrm{~Btu}/\mathrm{s} \end{aligned} \nonumber \]

Volumen

\[\begin{aligned} & 1 \mathrm{~m}^{3} = 1000 \mathrm{~L} = 10^{6} \mathrm{~cm}^{3} = 10^{6} \mathrm{~mL} = 35.315 \mathrm{~ft}^{3} = 264.17 \mathrm{~gal} \\ & 1 \mathrm{~ft}^{3} = 1728 \mathrm{~in}^{3} = 7.4805 \mathrm{~gal} = 0.028317 \mathrm{~m}^{3} \\ & 1 \mathrm{~gal} = 0.13368 \mathrm{~ft}^{3} = 0.0037854 \mathrm{~m}^{3} \end{aligned} \nonumber \]

Energía Específica

\[\begin{aligned} & 1 \mathrm{~kJ}/\mathrm{kg} = 1000 \mathrm{~m}^{2}/\mathrm{s}^{2} \\ & 1 \mathrm{~Btu}/\mathrm{lbm} = 25037 \mathrm{~ft}^{2}/\mathrm{s}^{2} \\ & 1 \mathrm{~ft} \cdot \mathrm{lbf}/\mathrm{lbm} = 32.174 \mathrm{~ft}^{2}/\mathrm{s}^{2} \end{aligned} \nonumber \]

Caudal Volumétrico

\[\begin{aligned} & 1 \mathrm{~m}^{3}/\mathrm{s} = 35.315 \mathrm{~ft}^{3}/\mathrm{s} = 264.17 \mathrm{~gal}/\mathrm{s} \\ & 1 \mathrm{~ft}^{3}/\mathrm{s} = 1.6990 \mathrm{~m}^{3}/\mathrm{min} = 7.4805 \mathrm{~gal}/\mathrm{s} = 448.83 \mathrm{~gal}/\mathrm{~min} \end{aligned} \nonumber \]

C.3 Modelos de Sustancias

Dos Modelos de Sustancias (Relaciones Constitutivas)
	Ecuación de Estado
	Modelo de Gas Ideal con calores específicos a temperatura ambiente	Modelo de Sustancia Incompresible con calores específicos a temperatura ambiente
Se utiliza para modelar el comportamiento de	gases y vapores	líquidos y sólidos
Supuestos básicos del modelo	La presión, el volumen y la temperatura obedecen a la relación ideal del gas:\[PV = NR_{u}T \nonumber \] La energía interna específica depende sólo de la temperatura,\(u = u(T)\). La masa molar de un gas ideal es igual a la masa molar de la sustancia real:\[M_{\text{ideal gas}} = M_{\text{real stuff}} \nonumber \] Los calores específicos son independientes de la temperatura, es decir, son constantes.	La densidad de la sustancia es una constante. La energía interna específica depende sólo de la temperatura,\(u = u(T)\). La masa molar de una sustancia incompresible es igual a la masa molar de la sustancia real:\[M_{\text{incomp substance}} = M_{\text{real stuff}} \nonumber \] Los calores específicos son independientes de la temperatura, es decir, son constantes.
\(P \ - \ T \ - \ \rho\)y\(P \ - \ T \ - \ \upsilon\) relaciones	\(P=\rho RT\)y\(P \upsilon = RT\) donde\(R = R_{u}/M\)	\(\upsilon = 1/\rho = \text{constant}\) Evaluado a temperatura ambiente
Relaciones térmicas específicas	\(c_{\text{p}} - c_{\text{v}} = R; \quad k = c_{\text{p}} / c_{\text{v}}\)	\(c_{\text{p}} = c_{\text{v}} = c, \text{ a constant}\)
\(c_{\text{p}}\)y\(c_{\text{v}}\) valores	Evaluado a temperatura ambiente	Evaluado a temperatura ambiente
\(\Delta u\)— energía interna específica	\(\Delta u = u_{2}-u_{1} = c_{\text{v}} \left(T_{2}-T_{1}\right)\)	\(\Delta u = u_{2}-u_{1} = c \left(T_{2}-T_{1}\right)\)
\(\Delta h\)— entalpía específica	\(\Delta h = h_{2}-h_{1} = c_{\text{p}} \left(T_{2} - T_{1}\right)\)	\[\begin{aligned} \Delta h &= h_{2}-h_{1} \\ &= \left(u_{2}+P_{2} \upsilon\right) - \left(u_{1}+P_{1} \upsilon\right) \\ &= \left(u_{2} - u_{1}\right) + \upsilon \left(P_{2}-P_{1}\right) \\ \text{thus}& \\ \Delta h &= \Delta u + \upsilon \Delta P = c \Delta T + \upsilon \Delta P \end{aligned} \nonumber \]
\(\Delta s\)— entropía específica Nota: Todas las temperaturas son valores absolutos, es decir\({ }^{\circ} \mathrm{R}\),\(\mathrm{K}\) o, en las relaciones de entropía	\[\begin{aligned} \Delta s &= s_{2}-s_{1} \\ &= c_{\text{p}} \ln \left(T_{2}-T_{1}\right) - R \ln \left(P_{2}-P_{1}\right) \\ &= c_{\text{v}} \ln \left(T_{2} / T_{1}\right) + R \ln \left(\upsilon_{2}-\upsilon_{1}\right) \end{aligned} \nonumber \]	\[\begin{aligned} \Delta s &= s_{2}-s_{1} \\ &= c \ln \left(T_{2}/T_{1}\right) \end{aligned} \nonumber \]

Ecuación de Gas Ideal
Bases Molares	Base Masiva
\[\begin{array}{c} PV=nRT \\ P \bar{\upsilon} = R_{u} T \quad \text{and} \quad P = \bar{\rho} R_{u} T \end{array} \nonumber \] \[\begin{aligned} \text{where} & \\ P &= \text{absolute pressure of gas } \left[\text{kPa or lbf} / \mathrm{ft}^{2}\right] \\ V &= \text{volume of gas } \left[\mathrm{m}^{3} \text{ or } \mathrm{ft}^{3}\right] \\ n &= \text{number of moles of gas } \left[\text{kmol or lbmol}\right] \\ R_{u} &= \text{universal gas constant (the same for every gas)} \\ &\quad\quad \left[ \mathrm{kJ}/\left(\mathrm{kmol} \cdot \mathrm{K}\right) \text{ or } \left(\mathrm{ft} \cdot \mathrm{lbf}\right) / \left(\mathrm{lbmol} \cdot { }^{\circ} \mathrm{R}\right) \right] \\ T &= \text{absolute temperature of gas } \left[\mathrm{K} \text{ or } { }^{\circ} \mathrm{R}\right] \\ \bar{\rho} &= \text{molar density} = 1/\bar{\upsilon} \ \left[\mathrm{kmol}/\mathrm{m}^{3} \text{ or } \mathrm{lbmol}/\mathrm{ft}^{3} \right] \\ \bar{\upsilon} &= \text{molar specific volume } \left[\mathrm{m}^{3}/\mathrm{kmol} \text{ or } \mathrm{ft}^{3}/\mathrm{lbmol}\right] \end{aligned} \nonumber \]	\[\begin{array}{c} PV=mRT \\ P \upsilon = RT \quad \text{and} \quad P = \rho R T \end{array} \nonumber \] \[\begin{aligned} \text{where} & \\ P &= \text{absolute pressure of gas } \left[\text{kPa or lbf} / \mathrm{ft}^{2}\right] \\ V &= \text{volume of gas } \left[\mathrm{m}^{3} \text{ or } \mathrm{ft}^{3}\right] \\ m &= \text{mass of gas } \left[\mathrm{kg} \text{ or } \mathrm{lbm}\right] \\ R &= \text{specific gas constant (different for each gas)} \\ &\quad\quad \left[\mathrm{kJ} / \left(\mathrm{kg} \cdot \mathrm{K}\right) \text{ or } \left(\mathrm{ft} \cdot \mathrm{lbf}\right) / \left(\mathrm{lbmol} \cdot { }^{\circ} \mathrm{R}\right) \right] \\ T &= \text{absolute temperature of gas } \left[\mathrm{K} \text{ or } { }^{\circ} \mathrm{R}\right] \\ \rho &= \text{density} = 1/\upsilon \ \left[ \mathrm{kg}/\mathrm{m}^{3} \text{ or } \mathrm{lbm}/\mathrm{ft}^{3} \right] \\ \upsilon &= \text{specific volume } \left[ \mathrm{m}^{3}/\mathrm{kg} \text{ or } \mathrm{ft}^{3}/\mathrm{lbm} \right] \end{aligned} \nonumber \]
\(\text{and}\) \[\begin{aligned} R_{u} &= 8.314 \ \frac{\mathrm{kJ}}{\mathrm{kmol} \cdot \mathrm{K}} = 8.314 \ \frac{\mathrm{J}}{\mathrm{mol} \cdot \mathrm{K}} \\ &= 1545 \ \frac{\mathrm{ft} \cdot \mathrm{lbf}}{\mathrm{lbmol} \cdot { }^{\circ} \mathrm{R}} \end{aligned} \nonumber \]	\(\text{and}\)\[ R = \frac{R_{u}}{M} \nonumber \] \(\text{where}\)\[\quad M = \text{molecular weight (molar mass) of a specific gas} \nonumber \]

Ecuación de Gas Ideal

Bases Molares

Base Masiva

\[\begin{array}{c} PV=nRT \\ P \bar{\upsilon} = R_{u} T \quad \text{and} \quad P = \bar{\rho} R_{u} T \end{array} \nonumber \]

\[\begin{aligned} \text{where} & \\ P &= \text{absolute pressure of gas } \left[\text{kPa or lbf} / \mathrm{ft}^{2}\right] \\ V &= \text{volume of gas } \left[\mathrm{m}^{3} \text{ or } \mathrm{ft}^{3}\right] \\ n &= \text{number of moles of gas } \left[\text{kmol or lbmol}\right] \\ R_{u} &= \text{universal gas constant (the same for every gas)} \\ &\quad\quad \left[ \mathrm{kJ}/\left(\mathrm{kmol} \cdot \mathrm{K}\right) \text{ or } \left(\mathrm{ft} \cdot \mathrm{lbf}\right) / \left(\mathrm{lbmol} \cdot { }^{\circ} \mathrm{R}\right) \right] \\ T &= \text{absolute temperature of gas } \left[\mathrm{K} \text{ or } { }^{\circ} \mathrm{R}\right] \\ \bar{\rho} &= \text{molar density} = 1/\bar{\upsilon} \ \left[\mathrm{kmol}/\mathrm{m}^{3} \text{ or } \mathrm{lbmol}/\mathrm{ft}^{3} \right] \\ \bar{\upsilon} &= \text{molar specific volume } \left[\mathrm{m}^{3}/\mathrm{kmol} \text{ or } \mathrm{ft}^{3}/\mathrm{lbmol}\right] \end{aligned} \nonumber \]

\[\begin{array}{c} PV=mRT \\ P \upsilon = RT \quad \text{and} \quad P = \rho R T \end{array} \nonumber \]

\[\begin{aligned} \text{where} & \\ P &= \text{absolute pressure of gas } \left[\text{kPa or lbf} / \mathrm{ft}^{2}\right] \\ V &= \text{volume of gas } \left[\mathrm{m}^{3} \text{ or } \mathrm{ft}^{3}\right] \\ m &= \text{mass of gas } \left[\mathrm{kg} \text{ or } \mathrm{lbm}\right] \\ R &= \text{specific gas constant (different for each gas)} \\ &\quad\quad \left[\mathrm{kJ} / \left(\mathrm{kg} \cdot \mathrm{K}\right) \text{ or } \left(\mathrm{ft} \cdot \mathrm{lbf}\right) / \left(\mathrm{lbmol} \cdot { }^{\circ} \mathrm{R}\right) \right] \\ T &= \text{absolute temperature of gas } \left[\mathrm{K} \text{ or } { }^{\circ} \mathrm{R}\right] \\ \rho &= \text{density} = 1/\upsilon \ \left[ \mathrm{kg}/\mathrm{m}^{3} \text{ or } \mathrm{lbm}/\mathrm{ft}^{3} \right] \\ \upsilon &= \text{specific volume } \left[ \mathrm{m}^{3}/\mathrm{kg} \text{ or } \mathrm{ft}^{3}/\mathrm{lbm} \right] \end{aligned} \nonumber \]

\(\text{and}\)

\[\begin{aligned} R_{u} &= 8.314 \ \frac{\mathrm{kJ}}{\mathrm{kmol} \cdot \mathrm{K}} = 8.314 \ \frac{\mathrm{J}}{\mathrm{mol} \cdot \mathrm{K}} \\ &= 1545 \ \frac{\mathrm{ft} \cdot \mathrm{lbf}}{\mathrm{lbmol} \cdot { }^{\circ} \mathrm{R}} \end{aligned} \nonumber \]

\(\text{and}\)\[ R = \frac{R_{u}}{M} \nonumber \]

\(\text{where}\)\[\quad M = \text{molecular weight (molar mass) of a specific gas} \nonumber \]

Datos de Propiedades Termofísicas para Algunas Sustancias Comunes (Unidades SI)
Gases (at\(25^{\circ} \mathrm{C}\) y\(1 \mathrm{~atm}\))
Sustancia		Masa molar	\(\dfrac{R}{\left[ \dfrac{\mathrm{kJ}}{\mathrm{kg} \cdot \mathrm{K}} \right]}\)	\(\dfrac{c_{v}}{\left[ \dfrac{\mathrm{kJ}}{\mathrm{kg} \cdot \mathrm{K}} \right]}\)	\(\dfrac{c_{p}}{\left[ \dfrac{\mathrm{kJ}}{\mathrm{kg} \cdot \mathrm{K}} \right]}\)	\(k\)	\(\dfrac{T_{c}}{\mathrm{K}}\)	\(\dfrac{P_{c}}{\mathrm{bar}}\)
Acetileno	\(\mathrm{C}_{2} \mathrm{H}_{2}\)	\(26.04\)	\(0.3193\)	\(1.37\)	\(1.69\)	\(1.23\)	\(309\)	\(62.4\)
Aire	—	\(28.97\)	\(0.2870\)	\(0.718\)	\(1.005\)	\(1.40\)	\(133\)	\(37.7\)
Amoníaco	\(\mathrm{NH}_{3}\)	\(17.04\)	\(0.4879\)	\(1.66\)	\(2.15\)	\(1.30\)	\(406\)	\(112.8\)
Dióxido de carbono	\(\mathrm{CO}_{2}\)	\(44.01\)	\(0.1889\)	\(0.657\)	\(0.846\)	\(1.29\)	\(304.2\)	\(73.9\)
Monóxido de carbono	\(\mathrm{CO}\)	\(28.01\)	\(0.2968\)	\(0.744\)	\(1.04\)	\(1.40\)	\(133\)	\(35.0\)
Etanos	\(\mathrm{C}_{2} \mathrm{H}_{6}\)	\(30.07\)	\(0.2765\)	\(1.48\)	\(1.75\)	\(1.18\)	\(305.4\)	\(48.8\)
Etileno	\(\mathrm{C}_{2} \mathrm{H}_{4}\)	\(28.05\)	\(0.2964\)	\(1.23\)	\(1.53\)	\(1.24\)	\(283\)	\(51.2\)
Helio	\(\mathrm{He}\)	\(4.003\)	\(2.077\)	\(3.12\)	\(5.19\)	\(1.67\)	\(5.2\)	\(2.3\)
Hidrógeno	\(\mathrm{H}_{2}\)	\(2.016\)	\(4.124\)	\(10.2\)	\(14.3\)	\(1.40\)	\(33.2\)	\(13.0\)
Metano	\(\mathrm{CH}_{4}\)	\(16.04\)	\(0.5183\)	\(1.70\)	\(2.22\)	\(1.31\)	\(190.7\)	\(46.4\)
Nitrógeno	\(\mathrm{N}_{2}\)	\(28.01\)	\(0.2968\)	\(0.743\)	\(1.04\)	\(1.40\)	\(126.2\)	\(33.9\)
Oxígeno	\(\mathrm{O}_{2}\)	\(32.00\)	\(0.2598\)	\(0.658\)	\(0.918\)	\(1.40\)	\ (154.4\	\(50.5\)
Propano	\(\mathrm{C}_{3} \mathrm{H}_{8}\)	\(44.09\)	\(0.1886\)	\(1.48\)	\(1.67\)	\(1.13\)	\(370\)	\(42.5\)
Refrigerante 134a	\(\mathrm{C}_{2} \mathrm{F}_{2} \mathrm{H}_{2}\)	\(102.03\)	\(0.08149\)	\(0.76\)	\(0.85\)	\(1.12\)	\(374.3\)	\(40.6\)
Agua (Vapor)	\(\mathrm{H}_{2} \mathrm{O}\)	\(18.02\)	\(0.4614\)	\(1.40\)	\(1.86\)	\(1.33\)	\(647.3\)	\(220.9\)

Líquidos				Sólidos*
Sustancia	Temp. \(({ }^{\circ} \mathrm{C})\)	\(\dfrac{\rho}{\left[ \dfrac{\mathrm{kg}}{\mathrm{m}^{3}}\right]}\)	\(\dfrac{c_{p}}{\left[ \dfrac{\mathrm{kJ}}{\mathrm{kg} \cdot \mathrm{K}} \right]}\)	Sustancia	\(\dfrac{\rho}{\left[ \dfrac{\mathrm{kg}}{\mathrm{m}^{3}}\right]}\)	\(\dfrac{c_{p}}{\left[ \dfrac{\mathrm{kJ}}{\mathrm{kg} \cdot \mathrm{K}} \right]}\)
Amoníaco	\(25\)	\(602\)	\(4.80\)	Aluminio	\(2,700\)	\(0.902\)
Benceno	\(20\)	\(879\)	\(1.72\)	Latón, amarillo	\(8,310\)	\(0.400\)
Salmuera\((20 \% \mathrm{NaCl})\)	\(20\)	\(1,150\)	\(3.11\)	Ladrillo (común)	\(1,922\)	\(0.79\)
Etanol	\(25\)	\(783\)	\(2.46\)	Concreto	\(2,300\)	\(0.653\)
Alcohol etílico	\(20\)	\(789\)	\(2.84\)	Cobre	\(8,900\)	\(0.386\)
Etilenglicol	\(20\)	\(1,109\)	\(2.84\)	Vidrio, ventana	\(2,700\)	\(0.800\)
Queroseno	\(20\)	\(820\)	\(2.00\)	Hierro	\(7,840\)	\(0.45\)
Mercurio	\(25\)	\(13,560\)	\(0.139\)	Plomo	\(11,310\)	\(0.128\)
Aceite (ligero)	\(25\)	\(910\)	\(1.80\)	Plata	\(10,470\)	\(0.235\)
Refrigerante 134a	\(25\)	\(1,206\)	\(1.42\)	Acero (suave)	\(7,830\)	\(0.500\)
Agua	\(25\)	\(997\)	\(4.18\)	* Evaluado a temperatura ambiente.
Valores adaptados de K. Wart, Jr. y D. E. Richards, Termodinámica, 6a ed. (McGraw-Hill, Nueva York, 1999) e Y. A. Cengul y M. A. Boles, Termodinámica, 4ta ed. (McGraw-Hill, Nueva York, 2002).

Datos de Propiedades Termofísicas para Algunas Sustancias Comunes (Unidades USCS)
Gases (at\(77^{\circ} \mathrm{F}\) y\(1 \mathrm{~atm}\))
Sustancia		Masa molar	\(\dfrac{R}{\left[ \dfrac{\mathrm{ft} \cdot \mathrm{lbf}}{\mathrm{lbm} \cdot { }^{\circ} \mathrm{R}} \right]}\)	\(\dfrac{c_{v}}{\left[ \dfrac{\mathrm{Btu}}{\mathrm{lbm} \cdot { }^{\circ} \mathrm{R}} \right]}\)	\(\dfrac{c_{p}}{\left[ \dfrac{\mathrm{Btu}}{\mathrm{lbm} \cdot { }^{\circ} \mathrm{R}} \right]}\)	\(k\)	\(\dfrac{T_{c}}{\text{ }^{\circ} \mathrm{R}}\)	\(\dfrac{P_{c}}{\mathrm{atm}}\)
Acetileno	\(\mathrm{C}_{2} \mathrm{H}_{2}\)	\(26.04\)	\(59.33\)	\(0.328\)	\(0.404\)	\(1.23\)	\(556\)	\(61.6\)
Aire	—	\(28.97\)	\(53.33\)	\(0.171\)	\(0.240\)	\(1.40\)	\(239\)	\(37.2\)
Amoníaco	\(\mathrm{NH}_{3}\)	\(17.04\)	\(90.67\)	\(0.397\)	\(0.514\)	\(1.29\)	\(730\)	\(111.3\)
Dióxido de carbono	\(\mathrm{CO}_{2}\)	\(44.01\)	\(35.11\)	\(0.156\)	\(0.202\)	\(1.29\)	\(548\)	\(72.9\)
Monóxido de carbono	\(\mathrm{CO}\)	\(28.01\)	\(55.16\)	\(0.178\)	\(0.249\)	\(1.40\)	\(239\)	\(34.5\)
Etanos	\(\mathrm{C}_{2} \mathrm{H}_{6}\)	\(30.07\)	\(51.38\)	\(0.353\)	\(0.419\)	\(1.19\)	\(549\)	\(48.2\)
Etileno	\(\mathrm{C}_{2} \mathrm{H}_{4}\)	\(28.05\)	\(55.08\)	\(0.294\)	\(0.365\)	\(1.24\)	\(510\)	\(50.5\)
Helio	\(\mathrm{He}\)	\(4.003\)	\(386.0\)	\(0.744\)	\(1.24\)	\(1.67\)	\(9.3\)	\(2.26\)
Hidrógeno	\(\mathrm{H}_{2}\)	\(2.016\)	\(766.4\)	\(2.43\)	\(3.42\)	\(1.40\)	\(59.8\)	\(12.8\)
Metano	\(\mathrm{CH}_{4}\)	\(16.04\)	\(96.32\)	\(0.407\)	\(0.531\)	\(1.30\)	\(344\)	\(45.8\)
Nitrógeno	\(\mathrm{N}_{2}\)	\(28.01\)	\(55.16\)	\(0.178\)	\(0.248\)	\(1.39\)	\(227\)	\(33.5\)
Oxígeno	\(\mathrm{O}_{2}\)	\(32.00\)	\(48.28\)	\(0.157\)	\(0.219\)	\(1.40\)	\(278\)	\(49.8\)
Propano	\(\mathrm{C}_{3} \mathrm{H}_{8}\)	\(44.09\)	\(35.04\)	\(0.355\)	\(0.400\)	\(1.13\)	\(666\)	\(42.1\)
Refrigerante 134a	\(\mathrm{C}_{2} \mathrm{F}_{4} \mathrm{H}_{2}\)	\(102.03\)	\(15.14\)	\(0.184\)	\(0.203\)	\(1.10\)	\(672.8\)	\(40.1\)
Agua (Vapor)	\(\mathrm{H}_{2} \mathrm{O}\)	\(18.02\)	\(87.74\)	\(0.335\)	\(0.445\)	\(1.33\)	\(1165\)	\(218.0\)

Líquidos				Sólidos*
Sustancia	Temp\(({ }^{\circ} \mathrm{F})\)	\(\dfrac{\rho}{\left[ \dfrac{\mathrm{lbm}}{\mathrm{ft}^{3}} \right]}\)	\(\dfrac{c_{p}}{\left[ \dfrac{\mathrm{Btu}}{\mathrm{lbm} \cdot { }^{\circ} \mathrm{R}} \right]}\)	Sustancia	\(\dfrac{\rho}{\left[ \dfrac{\mathrm{lbm}}{\mathrm{ft}^{3}} \right]}\)	\(\dfrac{c_{p}}{\left[ \dfrac{\mathrm{Btu}}{\mathrm{lbm} \cdot { }^{\circ} \mathrm{R}} \right]}\)
Amoníaco	\(80\)	\(37.5\)	\(1.135\)	Aluminio	\(170\)	\(0.215\)
Benceno	\(68\)	\(54.9\)	\(0.411\)	Latón, amarillo	\(519\)	\(0.0955\)
Salmuera\((20 \% \mathrm{NaCl})\)	\(68\)	\(71.8\)	\(0.743\)	Ladrillo (común)	\(120\)	\(0.189\)
Etanol	\(77\)	\(48.9\)	\(0.588\)	Concreto	\(144\)	\(0.156\)
Alcohol etílico	\(68\)	\(49.3\)	\(0.678\)	Cobre	\(555\)	\(0.0917\)
Etilenglicol	\(68\)	\(69.2\)	\(0.678\)	Vidrio, ventana	\(169\)	\(0.191\)
Queroseno	\(68\)	\(51.2\)	\(0.478\)	Hierro	\(490\)	\(0.107\)
Mercurio	\(77\)	\(847\)	\(0.033\)	Plomo	\(705\)	\(0.030\)
Aceite (ligero)	\(77\)	\(56.8\)	\(0.430\)	Plata	\(655\)	\(0.056\)
Refrigerante 134a	\(32\)	\(80.9\)	\(0.318\)	Acero (suave)	\(489\)	\(0.119\)
Agua	\(68\)	\(62.2\)	\(1.00\)	* Evaluado a temperatura ambiente.
Valores adaptados de K. Wart, Jr. y D. E. Richards, Termodinámica, 6a ed. (McGraw-Hill, Nueva York, 1999) e Y. A. Cengul y M. A. Boles, Termodinámica, 4ta ed. (McGraw-Hill, Nueva York, 2002).