List of Nomenclature

Author

DOFPro group

Purpose

This page is to test web versions of the nomenclature or variable names for the videos and the website.

Roman Symbols

Chosen Symbol	Description	F & R¹	SVN²	Ç & B³	H & R⁴
$a,\ b,\ c,\ d$	arbitrary constants or parameters in equations⁵	$a,\ b,\ c,\ d$	$A,\ B,\ C,\ D$		tbd
$a$	cubic equation of state parameter	$a$	$a$
$a$	acceleration, $\mathrm{m}/\mathrm{s}^2$	tbd	tbd	tbd	tbd
$a$	activity	$a$			$a$
$A$	area		$A$
$\mathrm{A}$	representative chemical species, e.g., $\mathrm{A} = \mathrm{CO_2},\ \mathrm{B} = \mathrm{H_2O}$				$A$
$\mathrm{A}_i$	ennumerated chemical species, e.g., $\mathrm{A}_1 = \mathrm{CO_2},\ \mathrm{A}_2 = \mathrm{H_2O}$				$A_i$
$A$	total Helmholtz energy				$A^t$
$\dot{A}$	total Helmholtz energy rate				$\dot{A}^t$
$\hat{A}$	molar Helmholtz energy				$A$
$\hat{A}$	specific Helmholtz energy				$A$
$b$	cubic equation of state parameter	$b$	$b$
$B$	second virial coefficient		$B$
$B^0$, $B^1$	functional values for generalized second-virial-coefficient correlation		$B^0$, $B^1$
$c$	number of independent chemical species, Gibbs phas rule	$c$	$N$
$c$	speed of sound		$c$
$C$	third virial coefficient		$C$
$C_\mathrm{A}$	concentration of representative chemical species $\mathrm{A}$	$C_A$			$C_i$
$C_i$	concentration of ennumerated chemical species $i$	$C_i$			$C_i$
$C_{\mathrm{A}_i}$	concentration of rectant A at time $t_i$ or in effluent from reactor $i$				$C_{\mathrm{A}_i}$
$C_p$	constant-pressure heat capacity	$C_p$			$C_p$
$C^\circ_p$	standard-state constant-pressure heat capacity
$C_v$	constant-volume heat capacity	$C_v$			$C_v$
$C$	third virial coefficient		$C$
$C^0$, $C^1$	functional values for generalized third-virial-coefficient correlation		$C^0$, $C^1$
$\langle C_p \rangle_H$	mena heat capacity for enthalpy calculations		$\langle C_P \rangle_H$
$\langle C_p \rangle_S$	mena heat capacity for enthalpy calculations		$\langle C_P \rangle_S$
$D$	diameter	$D$			$D_P$
$D$	fourth virial coefficient		$D$
$D_\mathrm{AB}$	binary diffusivity	$D$			$D_\mathrm{AB}$
$D_K$	Knudsen diffusivity				$D_\mathrm{K}$
$\mathscr{D}_c$	combined diffusivity				$\mathscr{D}_c$
$DF$	degrees of freedom, Gibbs phase rule	$DF$	$F$
$E_a$	energy or activation energy	$E_a$			$E$
$E_\mathrm{diffusion}$	activation energy for diffusion				$E_\mathrm{diffusion}$
$E_\mathrm{k}$	total kinetic energy	$E_\mathrm{k}$
$\hat{E}_\mathrm{k}$	specific or molar kinetic energy
$\dot{E}_\mathrm{k}$	total kinetic energy rate	$\dot{E}_\mathrm{k}$
$E_\mathrm{p}$	total potential energy	$E_\mathrm{p}$
$\hat{E}_\mathrm{p}$	specific or molar potential energy
$\dot{E}_\mathrm{p}$	total potential energy rate	$\dot{E}_\mathrm{p}$
$f$	fractional conversion	$f$			$f$
$f_i$	fugacity of pure species $i$ at system pressure $P$				$f_i^0$
$f^\circ_i$	standard state fugacity of species $i$		$f^\circ_i$
$\hat{f}_i$	fugacity of species i in solution		$\hat{f}_i$		$\hat{f}_i$
$f$	(Moody) friction factor⁶				$f_M$
$F$	force	$F$	$F$
$\hat{F}$	friction loss	$\hat{F}$
$\mathscr{F}$	Faraday’s constant		$\mathscr{F}$
$g$	standard gravitationa acceleration, $9.80665\ \mathrm{m/s^2}$				$g$
$g_c$	conversion from $\mathrm{lb_m}$ to $\mathrm{lb_f}$, $1 \equiv g_c = 32.1740 \mathrm{(lb_m)(ft)(lb_f)^{-1}(s)^{-2}}$	$g_c$	$g_c$
$G$	total Gibbs energy		$G^t$ or $nG$		$G$
$\dot{G}$	total Gibbs energy rate		$\dot{G}^t$ or $\dot{n}G$		$G$
$\hat{G}$	molar or specific Gibbs energy		$G$		$G$
$G^{\circ}_i$	standard state Gibbs energy of species $i$
$\bar{G}_i$	partial molar Gibbs energy of species $i$
$\hat{G}^E$	excess Gibbs energy $\equiv \hat{G} - \hat{G}^{id}$
$\hat{G}^R$	residual Gibbs energy $\equiv \hat{G} - \hat{G}^{ig}$
$\Delta \hat{G}$	molar or specific Gibbs energy change of mixing		$\Delta G$
$\Delta \hat{G}^\circ$	molar or specific standard Gibbs eneergy energy change of reaction		$\Delta G^\circ$
$\Delta \hat{G}^\circ_f$	molar or specific standard Gibbs energy change of formation		$\Delta G^\circ_f$
$h$	convective heat transfer coefficient	$h$			$h_c$
$h_i$	Thiele modulus for $i$th-order reaction				$h_i$
$h_\mathrm{T}$	Thiele modulus				$h_\mathrm{T}$
$H_A$	Henry’s law constant for chemical species $A$	$H_A$	$\mathscr{H}_A$		$H$
$H$	total enthalpy	$H$	$H^t$ or $nH$
$\dot{H}$	total enthalpy rate	$\dot{H}$	$\dot{H}^t$ or $\dot{n}H$
$\hat{H}$	molar or specific enthalpy	$\hat{H}$	$H$		$h$
$H^{\circ}_i$	standard state enthalpy of species $i$
$\bar{H}_i$	partial molar enthalpy of species $i$
$\hat{H}^E$	excess enthalpy $\equiv \hat{H} - \hat{H}^{id}$
$\hat{H}^R$	residual enthalpy $\equiv \hat{H} - \hat{H}^{ig}$
$(\hat{H}^R)^0,\ (\hat{H}^R)^1$	generalized residual-enthalpy correlation functions		$(H^R)^0,\ (H^R)^1$
$\Delta \hat{H}$	molar or specific enthalpy change of mixing		$\Delta H$
$\Delta \hat{H}^\circ$	molar or specific standard enthalpy energy change of reaction		$\Delta H^\circ$
$\Delta \hat{H}^\circ_f$	molar or specific standard enthalpy change of formation		$\Delta H^\circ_f$
$J$	molar flux				$N$
$k_0$	pre-exponential, frequency factor, or steric factor	$k_0$			$A$
$k$	reaction rate coefficient				$k$
$k$	thermal conductivity	$k$			$\kappa$
$k$	Boltzmann constant		$k$		$k_B$
$k_m$	mass transfer coefficient				$k_m$
$K$	equilibrium constant	$K$	$K$		$K$
$K_j$	equilibrium constant for reaction $j$		$K_J$
$K_0, K_1, K_2$	equilibrium constant factors, $K = K_0K_1K_2$		$K_0, K_1, K_2$
$K_i$	$K$-value, vapor/liquid equilibrium ratio, $K_i \equiv y_i/x_i$		$K_i$
$K$	Michaelis constant				$K$
$K_i$	adsorption equilibrium constant				$K_i$
$K_p$	equilibrium constant expressed in terms of partial pressures				$K_p$
$K_r$	equilibrium constant for surface reaction expressed in terms of fractional surface coverages $\theta_i$				$K_r$
$l$	length	$L$	$l$
$L$	reactor length				$L$
$L$, $N$	average chain length				$L$
$\bar{L}$	average pore length				$\bar{L}$
$\mathcal{L}$	molar fraction of system that is liquid		$\mathscr{L}$
$m$	mass	$n$			$m$
$\textbf{M}$	Mach number		$\textbf{M}$
$n$	overall order of reaction				$m$
$\dot{m}$	mass flow rate	$\dot{m}$			$\dot{m}$
$M$	molecular weight or molar mass⁷	$M$			$M$
$n$	reaction order	$n$			$\beta_i$
$n$	number of moles	$n$			$n$, $N$
$\dot{n}$	molar flow rate	$\dot{n}$			$F$
$n_i$	moles of unspecified species $i$	$n_i$	$n_i$		$n_i$, $N_i$
$n_\mathrm{A}$	moles of specific species $\mathrm{A}$, e.g., $n_\mathrm{CO_2}$				$n_i$
$N_A$	Avogadro’s number		$N_A$		$N_0$
$Pe$	Péclet number				$N_\mathrm{Pe}$
$Re$	Reynolds number	$Re$	$\mathrm{Re}$		$N_\mathrm{Re}$
$Sc$	Schmidt number				$N_\mathrm{Sc}$
$Sh$	Sherwood number				$N_\mathrm{Sh}$
$P$	pressure	$P$			$P$
$P_\mathrm{c}$	critical pressure	$P_\mathrm{c}$	$P_c$		$P_c$
$P_\mathrm{r}$	reduced pressure, $P/P_c$	$P_\mathrm{r}$
$p_\mathrm{A}$	partial pressure of species A	$p_\mathrm{A}$
$p^*_\mathrm{A}(T)$	saturation or vapor pressure at temperature $T$	$p^*_\mathrm{A}(T)$	$P^\mathrm{sat}_i$		$P_0$
$e^-$	charge on an electron				$q$
$Q$	heat transferred from surroundings to system	$Q$			$Q$
$\dot{Q}$	heat transfer rate from surroundings to system	$\dot{Q}$	$\dot{Q}$		$q$
$Q_r$	rate at which (mainly thermal) energy is removed from a chemical reactor				$Q_r$
$Q_g$	rate at which thermal energy is generated by an exothermic chemical reaction				$Q_g$
$\dot{Q}$	rate of heat transfer from surroundings to system	$\dot{Q}$			$\dot{Q}$
$r$	number of independent chemical equations, Gibbs phase rule	$r$	$r$
$r$	compression ratio		$r$
$r_p$	pressure ratio
$r$	radius	$r$	$r$		$r$
$r$	reaction rate, $r = 1/(\nu_i V)\ dn_i/dt$	$r$			$r$
$-r_\mathrm{A}$	rate of disappearance of species $\mathrm{A}$				$−r_\mathrm{A}$
$r_i$	rate of appearance of species i				$r_i$
$\bar{r}$	average pore radius				$\bar{r}$
$R$	gas constant	$R$			$R$
$R$	recycle ratio				$R$
$S$	total entropy	$S$	$S^t$
$\dot{S}$	total entropy rate
$\hat{S}$	molar or specific entropy	$\hat{S}$	$S$	$s$
$\bar{S}_i$	partial molar entropy of species $i$		$\bar{S}_i$
$\hat{S}^E$	excess entropy $\equiv \hat{S} - \hat{S}^{id}$
$\hat{S}^R$	residual entropy $\equiv \hat{S} - \hat{S}^{ig}$
$(\hat{S}^R)^0,\ (\hat{S}^R)^1$	generalized residual-entropy correlation functions		$(S^R)^0,\ (S^R)^1$
$S_G$	total entropy generation	$S$	$S^t$
$\dot{S_G}$	total entropy generation rate
$\Delta \hat{S}$	molar or specific entropy change of mixing		$\Delta S$
$\Delta \hat{S}^\circ$	molar or specific standard entropy change of reaction		$\Delta S^\circ$
$\Delta \hat{S}^\circ_f$	molar or specific standard entropy change of formation		$\Delta S^\circ_f$
$S$	sample standard deviation (statistics)
$S^2$	sample variance
$S$	selectivity	$\mathrm{Selectivity}$			$S$
$S$	space velocity				$S$
$S, A$	surface area⁸				$S$
$S_g$	specific surface area of catalyst				$S_g$
$S_0$	initial substrate concentration				$S_0$
$S_x$	gross geometric surface area of catalyst pellet				$S_x$
$\mathrm{SCMH}$	standard cubic meters per hour	$\mathrm{SCMH}$
$\mathrm{SCLH}$	standard cubic liters per hour	$\mathrm{SCLH}$
$\mathrm{SCFH}$	standard cubic feet per hour	$\mathrm{SCFH}$
$\mathrm{SG}$	specific gravity	$\mathrm{SG}$
$t$	time				$t$
$t_f$	time to achieve a specified fraction conversion $f$				$t_f$
$t_i$	time at which reactant concentration $C_{\mathrm{A}_i}$ is measured				$t_i$
$\bar{t}$	mean residence time				$\bar{t}$
$T$	temperature (usually absolute)	$T$			$T$
$T_m$	melting point temperature	$T_m$
$T_b$	boiling point temperature	$T_b$
$T_\sigma$	surroundings, background, or ambient temperature		$T_\sigma$
$T_\mathrm{c}$	critical temperature	$T_\mathrm{c}$	$T_c$		$T_C$
$T_\mathrm{r}$	reduced temperature, $T/T_\mathrm{c}$	$T_\mathrm{r}$
$u$	linear velocity	$u$			$u$
$U$	overall heat transfer coefficient	$U$			$U$
$U$	total internal energy	$U$
$\dot{U}$	total internal energy rate	$\dot{U}$
$\hat{U}$	molar internal energy	$\hat{U}$
$\hat{U}$	specific internal energy	$\hat{U}$
$\Delta \hat{U}$	molar or specific internal energy change of mixing	$\Delta \hat{U}$
$\Delta \hat{U}^\circ$	molar or specific standard internal energy change of reaction	$\Delta \hat{U}^\circ$
$\Delta \hat{U}^\circ_f$	molar or specific standard internal energy change of formation	$\Delta \hat{U}^\circ_f$
$v$	volume of gas adsorbed				$v$
$v_m$	volume of gas adsorbed in a monolayer				$v_m$
$V$	total volume	$V$			$V$
$\dot{V}$	volumetric flow rate	$\dot{V}$
$\hat{V}_\mathrm{c}$	molar or specific critical volume	$\hat{V}_\mathrm{c}$	$V_c$
$\hat{V}$	molar volume, $V/n$, or specific volume, $V/m$	$\hat{V}$	$V$	$v$	tbd
$\Delta \hat{V}$	molar or specific volume change of mixing
$V_g$	void volume per gram of catalyst				$V_g$
$V_p$	gross geometric volume of catalyst pellet				$V_p$
$V$	reactor volume				$V_R$
$V_R$	volume of solid catalyst				$V'$
$\dot{V}$	volumetric flow rate	$\dot{V}$	$\dot{V}$, $q$		$\mathscr{V}$
$\mathcal{V}$	molar fraction of system that is vapor		$\mathscr{V}$
$W$	weight of solid catalyst				$W$
$W$	work done by surroundings on system⁹	$W$	$W$	$-W,\ W$	$-W$
$\dot{W}_\mathrm{s}$	rate at which shaft work is done on system¹⁰	$\dot{W}_\mathrm{s}$	$\dot{W}_\mathrm{s}$	$-\dot{W}_\mathrm{s}$, $\dot{W}_\mathrm{s}$	$-\dot{W}$
$W_\mathrm{ideal}$	ideal work		$W_\mathrm{ideal}$
$\dot{W}_\mathrm{ideal}$	ideal work rate		$\dot{W}_\mathrm{ideal}$
$W_\mathrm{lost}$	lost work		$W_\mathrm{lost}$
$\dot{W}_\mathrm{lost}$	lost work rate		$\dot{W}_\mathrm{lost}$
$x_i$	mass or mole fraction of unspecified species $i$¹¹	$x_i$	$x_i$	$x_i$	$x_i$
$x_i$	$i$th experimental measurement or data point $i$¹²	$x$
$y_i$	mass or mole fraction of unspecified species $i$¹³	$y_i$	$y_i$
$y_i$	$i$th experimental measurement or data point $i$¹⁴	$y$
$z_i$	mass or mole fraction of unspecified species $i$¹⁵, usually overall	$z_i$	$z_i$		$x$
$x$	distance from pore mouth				$x$
$x_c$	distance from pore mouth at which reactant concentration vanishes				$x_c$
$y$	instantaneous fractional yield	$\mathrm{Yield}$			$y$
$Y$	overall yield coefficient				$Y_{X/S}$
$Y_\mathrm{R}$	overall fractional yield of species R				$Y_\mathrm{R}$
$z$	elevation above a datum		$z$
$Z$	distance from inlet of tubular reactor				$Z$
$z$	compressibility, $z \equiv P\hat{V}/(RT)$	$z$	$Z$
$z_\mathrm{c}$	critical compressibility, $z_\mathrm{c} \equiv P_\mathrm{c}\hat{V}_\mathrm{c}/(RT_\mathrm{c})$	$z_\mathrm{c}$	$Z_c$
$z^0,\ z^1$	generalized compressibiliity-factor correlation functions		$Z^0,\ Z^1$

Greek Symbols

Chosen Symbol	Description	F & R	SVN	Ç & B	H & R
$\alpha$	Soave–Redlich–Kwong equation of state parameter, $\alpha = [1+(0.48508+1.55171\omega-0.1561 \omega^2)(1+\sqrt{T_\mathrm{r}})]$	$\alpha$	$\alpha$
$\alpha$	area covered per molecule adsorbed				$\alpha$
$\beta$	energy conversion function used in determination of the effectiveness factor for a nonisothermal catalyst pellet				$\beta$
$\beta$	volume expansivity
$\gamma$	activity coefficient				$\gamma$
$\gamma$	ratio of heat capacities, $\gamma \equiv C_p/C_v$		$\gamma$	$k$
$\gamma_i$	activity coefficient of species $i$ in solution
$\delta$	volumetric expansion parameter				$\delta_\mathrm{A}$
$\Delta$	difference, e.g., $out-in$ or $final-initial$	$\Delta$	$\Delta$	$\Delta$	$\Delta$
$\epsilon_B$	bed porosity				$\epsilon_B$
$\epsilon_p$	porosity of pellet or particle				$\epsilon_p$
$\epsilon_\mathrm{total}$	total porosity of packed bed				$\epsilon_\mathrm{total}$
$\epsilon$	emissivity of solid				$\epsilon$
$\eta$	catalyst effectiveness factor				$\eta$
$\eta$	thermal efficiency
$\theta_i$	fraction of catalyst surface covered by species i				$\theta_i$
$\theta_v$	fraction of surface sites that are vacant				$\theta_v$
$\lambda$	mean free path				$\lambda$
$\mu$	true mean or population mean (statistics)
$\mu$	dynamic viscosity, e.g, $\mathrm{Pa}\cdot\mathrm{s}$				$\mu$
$\mu_i$	chemical potential of species $i$				$\mu_i$
$\nu$	kinematic viscosity, e.g., $\mathrm{m^2/s}$				$\nu$
$\nu_\mathrm{A}$	stoichiometric coefficient for species $\mathrm{A}$, e.g., $\nu_{\mathrm{CO_2}}$	$\nu_\mathrm{A}$	$\nu_\mathrm{A}$		$\nu_\mathrm{A}$
$\nu_i$	stoichiometric coefficient for unspecified species $i$	$\nu_i$	$\nu_i$		$\nu_i$
$\xi$	extent of reaction, reaction coordinate	$\xi$	$\epsilon$		$\xi$
$\dot{\xi}$	extent of reaction rate	$\dot{\xi}$	$\dot{\epsilon}$
$\displaystyle\prod_i$	product of the $i$ terms that follow				$\displaystyle\prod_i$
$\rho$	density or mass concentration	$\rho$		$\rho_\mathrm{A}$	mass concentration of species A
$\rho_B$	bulk density of catalyst				$\rho_B$
$\sigma$	true or population standard deviation (statistics)
$\sigma^2$	true or population variance (statistics)
$\sigma$	surface tension		$
$\sigma$	surface site				$\sigma$
$\sigma^2$	variance of residence-time distribution curve				$\sigma^2$
$\Pi$	number of equilibrium phases	$\Pi$	$\pi$
$\displaystyle\sum_i$	sum of the $i$ terms that follow				$\displaystyle\sum_i$
$\tau$	reactor space time				$\tau$
$\tau_i$	space time for reactor $i$				$\tau_i$
$\tau_{1/2}$	reaction half-life				$\tau_{1/2}$
$\tau'$	tortuosity factor				τ′
$\phi_i$	fugacity coefficient for species $i$		$\hat{\phi}_i$		$(f/P)_i$
$\hat{\phi}_i$	fugacity coefficient for species $i$ in solution		$\phi_i$		$(f/P)_i$
$\phi^0,\ \phi^1$	generalized compressibiliity-factor correlation functions		$\phi^0,\ \phi^1$
$\phi_Ln$	Thiele modulus for an infinite flat plate catalyst, $n$th order reaction
$\phi_Sn$	Thiele modulus for a spherical catalyst, $n$th order reaction
$\omega$	Pitzer acentric factor	$\omega$	$\omega$

Subscripts

Chosen Symbol	Description	H & R
$\mathrm{A}$	generalized chemical species A	A
$\mathrm{batch}$	associated with a batch reactor	batch
tbd	bulk fluid property	B
tbd	associated with the growth cycle of a microorganism	cycle
tbd	associated with cell death	d
tbd	equilibrium	e
tbd	endogenous metabolism	em
tbd	effective	eff
tbd	effluent stream property or equilibrium property	E
tbd	external surface of catalyst pellet	ES
$f$	refers to reactions involving formation of a compound from its elements	f
$f$	refers to forward reaction	f
tbd	property evaluated at final or effluent conditions	F
tbd	fed batch	FB
tbd	gas phase	g
tbd	refers to species i, reaction i, or reactor i in a CSTR network	i
$\mathrm{in}$	refers to inlet stream property	in
tbd	liquid phase	l
tbd	lag time for growth of microorganism	lag
tbd	refers to limiting reagent	lim
tbd	property value at end of catalyst pore or in longitudinal direction	L
tbd	property value per unit mass of catalyst	m
tbd	maximum or extremum value	max
tbd	mass transfer	MT
tbd	property value leaving reactor n	n
tbd	net specific biomass growth rate associated with the logistic model	net
tbd	associated with the times during the production cycle when a biochemical reaction is not occurring	nonproductive
$\mathrm{out}$	refers to outlet stream property	out
tbd	pellet or particle value	p
tbd	pseudo equilibrium	PE
tbd	reverse reaction	r
tbd	reaction or property value in radial direction	R
tbd	rate-limiting step	RLS
tbd	half-saturation constant in Monod rate law	S
tbd	solid	S
tbd	substrate	S
tbd	steady state	SS
tbd	stationary phase	SP
tbd	system	sys
tbd	tube	T
tbd	property value per unit volume of catalyst bed
tbd	wall
tbd	defines the substances associated with the yield coefficient	X/S
tbd	property value in longitudinal direction	z
tbd	property value at time zero, reactor inlet, or at mouth of catalyst pore	0
tbd	value at infinite time	∞
tbd	in the logistic model, this symbol refers to the infinite time mass of the microorganism	∞

Superscripts

Chosen Symbol	Description	H & R
tbd	refers to variables associated with standard states of materials	0
tbd	variable is expressed per unit surface area	″
tbd	variable is expressed per unit volume of solid catalyst	″′
tbd	refers to variable associated with transition state	‡
tbd	average value of property	ˆ

Other Diacritical marks

Chosen Symbol	Description	H & R
$\bar{ }$	average or arithmetic mean (statistics)	0
$\bar{ }$	partial molar quantity	0
$\hat{ }$	specific or molar quantity, e.g., $\hat{V} = V/n$	″
$\hat{ }$	property in solution, e.g., $\hat{\phi}_i =$ fugacity coefficient of species $i$ in solution	″′
$\dot{ }$	rate or 1st derivative w.r.t. time, e.g., $\dot{m} =$ mass flow rate or $dm/dt$	‡
$\langle\ \rangle$	average value of property	ˆ

Not Referenced Symbols

Chosen Symbol	Description	H & R
tbd	external (superficial) surface area	$a$
tbd	cell growth coefficients	$a,\ a',\ a''$
tbd	gas–liquid interfacial area per unit volume of liquid	$a_V$
tbd	hypothetical concentration of gas in the liquid phase	$C^*_l$
tbd	reactant concentration at time zero in a CSTR operating under transient conditions	$C^*$
tbd	dispersion or diffusivity parameter	$\mathscr{D}$
tbd	pseudo-binary diffusivity of species A in a multicomponent gas mixture	$\mathscr{D}_{\mathrm{A}m}$
tbd	relative kinetic energy directed along the line of centers in a collision (on a per mole basis)	$E_c$
tbd	energy increase accompanying reaction at absolute zero	$E_0$
tbd	initial enzyme concentration	$E_0$
tbd	parameter used in analysis of the activated sludge process	φ
tbd	concentration-dependent portion of reaction rate expression	φ(Ci)
tbd	molal flow rate	$F$
tbd	hypothetical molal flow rate of species A corresponding to a stream in which none of the A has reacted	$F′_\mathrm{A}$
tbd	cumulative residence time distribution function	$F(t)$
tbd	ratio of reaction rate for poisoned catalyst to that for unpoisoned catalyst	$\mathscr{F}$
tbd	gas phase	g
tbd	mass velocity	$G$
tbd	Thiele modulus for poisoned catalyst	$h_p$
tbd	Chilton–Colburn factor for mass transfer	$j_D$
tbd	Chilton–Colburn factor for heat transfer	$j_H$
tbd	Molar flux of species $i$ relative to the molar average velocity	$J_i$
tbd	pseudo first-order rate constant for cell death	$k_d$
tbd	pseudo first-order rate constant for endogenous metabolism	$k_{em}$
tbd	rate constant for acid-catalyzed reaction	$k_\mathrm{H^+}$
tbd	rate constant in infinitely dilute solution or for uncatalyzed reaction	$k_0$
tbd	rate constant for base-catalyzed reaction	$k_\mathrm{OH^-}$
tbd	pseudo rate constant for desorption	$k'$
tbd	half-saturation constant	$K_S$
tbd	dissociation constant for water	$K_w$
tbd	liquid phase	l
tbd	parameter involved in definition of termolecular collisions	$l$
tbd	maintenance coefficient for cell	$m_S$
tbd	mass of tracer injected as a pulse stimulus	$m_T$
tbd	number of cells	$n$
tbd	number of possible adsorption layers	$n$
tbd	number of viable cells at the time the death phase of the cell growth cycle begins	$n^*$
tbd	number density of molecules of species i	$n'_i$
tbd	number of pores per catalyst particle	$n_p$
tbd	number of cells in the inoculum	$n_0$
tbd	number of cells at the start of the exponential growth phase of the cell growth cycle	$n^*_0$
tbd	steric probability factor	$P_S$
tbd	productivity	$\mathscr{P}$
tbd	parameter representing the combined effects of static pressure and gravitational force	$\mathscr{P}$
tbd	thermal conductivity of bulk fluid	$k_f$
tbd	mass transfer coefficient for the gas phase	$k_g$
tbd	mass transfer coefficient defined	$k_G$
tbd	mass transfer coefficient for the liquid phase	$k_l$
tbd	maintenance coefficient	$k_m$
tbd	mass transfer coefficient	$k_m$
tbd	equilibrium constant for reaction expressed in terms of activities	$K_a$
tbd	overall liquid phase mass transfer coefficient	$K_l$
tbd	number of CSTR reactors in cascade	$N$
tbd	number of moles of species A at the start of a batch reaction	$N_{\mathrm{A}0}$
tbd	number of moles of species $i$ contained within a reactor	$N_i$
tbd	diffusive flux in radial direction	$N_r$
tbd	transfer function variable	$p$
tbd	number of stirred-tank reactors in a cascade	$n$
tbd	heat evolved in Semenov’s correlation of activation energies and the exothermicity of reactions of small atoms and radicals	$q$
tbd	heat flux	$q$
tbd	heat transfer rate	$q$
tbd	biomass specific q-rate	$q_S$
tbd	partition function	$Q$
tbd	rate of disappearance of species A in CSTR $i$	$−r_{\mathrm{A}i}$
tbd	biomass specific growth rate for species i	$r_{ix}$
tbd	rate of disappearance of substrate per unit of biomass	$−r_{S,m}$
tbd	rate of disappearance of substrate per unit of biomass evaluated at the effluent conditions	$−r_{S,\mathrm{out}}$
tbd	reaction rate employed in pseudo homogeneous models of packed-bed reactors	$r_v$
tbd	reaction rate in a constant volume system	$r_v$
tbd	interatomic separation distance between atoms $X$ and $Y$	$r_{xy}$
tbd	rate of production of X per unit of biomass	$r_X$
tbd	lag time associated with the growth cycle for microorganisms	$t_\mathrm{lag}$
tbd	shutdown time in batch reactor	$t_s$
tbd	time elapsed since the start of the stationary phase	$t_\mathrm{SP}$
tbd	radius	$R$
tbd	total rate of consumption of limiting substrate	$-\mathscr{R}_S$
tbd	total rate of production of biomass	$\mathscr{R}_X$
tbd	concentration of limiting substrate	$s$
tbd	number of squared terms contributing to the activation energy of a reaction	$S$
tbd	instantaneous yield coefficient in a biochemical reaction	$y_{X/S}$
tbd	bimolecular collision frequency for molecules A and B	$Z_\mathrm{AB}$
tbd	termolecular collision frequency	$Z_\mathrm{ABC}$
tbd	number (and sign) of charges on ion I	$Z_i$
tbd	total quantity of limiting substrate	$S$
tbd	relaxation time	$t^*$
tbd	time corresponding to the end of the acceleration phase of the cell growth cycle	$t^*$
tbd	time at which the death phase of the cell growth cycle begins	$t^*_{d0}$
tbd	ratio of reactor length to average linear velocity	$\bar{t}^*$
tbd	concentration of biomass	$x$
tbd	temperature at center of catalyst pellet or critical temperature	$T_C$
tbd	temperature of heat source or sink	$T_m$
tbd	average molecular velocity	$\bar{v}$
tbd	velocity with which activated complexes move from left to right across the transition state	$\vec{v}^\ddagger$
tbd	velocity of an enzymatic reaction	$V$
tbd	volumetric flow rate at inlet of reactor network	$\mathscr{V}_0$
tbd	weight fraction	$w$
tbd	normalized pressure ($P/P_0$)	$x$
tbd	total mass of live cells	$X$
tbd	total mass of live cells when the biochemical reaction ceases	$X_F$
tbd	mass of live cells at the start of the stationary phase	$X_{\mathrm{S}_0}$
tbd	mass of cells at infinite time in the logistic model	$X_\infty$
tbd	branching coefficient in chain reaction mechanism	$\alpha$
tbd	coefficient in Luedeking–Piret equation	$\alpha$
tbd	dimensionless concentration variable	$\alpha$
tbd	fraction of catalyst surface that is poisoned	$\alpha$
tbd	dimensionless concentration variable for competitive consecutive reactions [defined by equation (5.4.18)]	$\beta$
tbd	coefficient in Luedeking–Piret equation	$\beta$
tbd	order of the reaction with respect to species i	$\beta_i$
tbd	Arrhenius number	$\gamma$
tbd	reaction progress variable for consecutive reactions	$\delta^*$
tbd	characteristic length dimension of the transition state	$\delta^\neq$
tbd	time separating rate measurements	$\Delta$
tbd	deviation from equilibrium conditions	$\Delta \xi^*$
tbd	rate of dissipation of turbulent energy	$\epsilon$
tbd	relative kinetic energy directed along the line of centers in a collision	$\epsilon_c$
tbd	ratio of rate constants for consecutive reactions	$\kappa$
tbd	generalized physical property	$\lambda$
tbd	Kolmogorov number	$\lambda$
tbd	specific growth rate	$\mu$
tbd	ionic strength	$\mu$
tbd	reduced mass	$\mu_\mathrm{AB}$
tbd	maximum specific growth rate	$\mu_\mathrm{max}$
tbd	net specific growth rate	$\mu_\mathrm{net}$
tbd	specific rate of replication	$\mu_R$
tbd	extent of reaction per unit volume in constant-volume systems	$\xi^*$
tbd	Hammett reaction constant	$\rho_i$
tbd	hard-sphere diameter for molecule $i$	$\sigma_i$
tbd	Hammett substituent constant	$\sigma_i$
tbd	effective hard-sphere diameter for bimolecular collision	$\sigma_\mathrm{AB}$
tbd	space time for a cascade of CSTR reactors	τc
tbd	proportionality constant associated with deviation of the Hammett equation	τN
tbd	space time for a plug flow reactor	τp
tbd	dimensionless time variable for competitive consecutive reactions	τ*

Footnotes

Elementary Principles of Chemical Processes, 4th Edition, Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard, ISBN: 978-1-119-19210-7, December 2018↩︎
Introduction to Chemical Engineering Thermodynamics, 9th Edition, Hendrick Van Ness, Michael Abbott, J.M. Smith, Mark Swihart, 2022, ISBN10: 1260721477 | ISBN13: 9781260721478↩︎
Thermodynamics: An Engineering Approach Edition: 9th, Yunus Çengel, Michael Boles, 2019, ISBN10:1260920445↩︎
Introduction to Chemical Engineering Kinetics & Reactor Design, 2nd Ed. Hill & Root, Wiley. ISBN: 978-1-118-36825-1↩︎
For example, $C_p= a + bt + cT^2 + dT^3$ where $a$, $b$, $c$, and $d$ are empirical constants.↩︎
There are two common friction factors in use. Mechanical Engineers tend to use the Moody friction factor, also known as the Darcy or Blasius friction factor. Chemical Engineers tend to use the Fanning friction factor. $f_\mathrm{Fanning} = f_\mathrm{Moody}/4$. Be sure to identify which friction factor your tables, charts, and equations use.↩︎
There are subtle distictions between molar mass, molecular mass, and molecular weight. For a fairly full discussion read Wikipedia: Molar mass ↩︎
$S$ is normally used when referring to the total surface area of a catalyst pellet or porous solid. $A$ is normally used for other surface areas, such as a sphere, tube, or reactor.↩︎
The standard sign convention for Mechanical Engineering is that work out is positive. The modern sign convention for Chemical Engineering is that work out is negative. Çengel and Boles choose whatever sign convention they feel makes the problem easiest.↩︎
The standard sign convention for Mechanical Engineering is that work out is positive. The modern sign convention for Chemical Engineering is that work out is negative. Çengel and Boles choose whatever sign convention they feel makes the problem easiest.↩︎
Often you have to determine from context what sort of fraction it is. When discussing the relationship between mass and mole fractions, $x_i$ is often used for the mass fraction of species $i$ and $y_i$ for mole fraction of species $i$. When discussing vapor/liquid equlibrium, $x_i$ is used for the liquid-phase mass or mole fraction of species $i$ and $y_i$ is used for the corresponding vapor-phase fraction of species $i$. $z_i$ is most often used as the overall mass or mole fraction of species $i$ in a mixture of vapor and liquid. In such cases, $x_i$ is used for the mass or mol fraction of species $i$ in the liquid, and $y_i$ is used for the mass or mol fraction of species $i$ in the vapor.↩︎
In statistics, $x_i$ is the $i$th measurement or data point and $\bar{x}$ is the arithmetic mean of the data points. For data pairs, $x_i$ is the $i$th independent or specified value, and $y_i$ is the $i$th dependent or measured value.↩︎
Often you have to determine from context what sort of fraction it is. When discussing the relationship between mass and mole fractions, $x_i$ is often used for the mass fraction of species $i$ and $y_i$ for mole fraction of species $i$. When discussing vapor/liquid equlibrium, $x_i$ is used for the liquid-phase mass or mole fraction of species $i$ and $y_i$ is used for the corresponding vapor-phase fraction of species $i$. $z_i$ is most often used as the overall mass or mole fraction of species $i$ in a mixture of vapor and liquid. In such cases, $x_i$ is used for the mass or mol fraction of species $i$ in the liquid, and $y_i$ is used for the mass or mol fraction of species $i$ in the vapor.↩︎
In statistics, $x_i$ is the $i$th measurement or data point and $\bar{x}$ is the arithmetic mean of the data points. For data pairs, $x_i$ is the $i$th independent or specified value, and $y_i$ is the $i$th dependent or measured value.↩︎
Often you have to determine from context what sort of fraction it is. When discussing the relationship between mass and mole fractions, $x_i$ is often used for the mass fraction of species $i$ and $y_i$ for mole fraction of species $i$. When discussing vapor/liquid equlibrium, $x_i$ is used for the liquid-phase mass or mole fraction of species $i$ and $y_i$ is used for the corresponding vapor-phase fraction of species $i$. $z_i$ is most often used as the overall mass or mole fraction of species $i$ in a mixture of vapor and liquid. In such cases, $x_i$ is used for the mass or mol fraction of species $i$ in the liquid, and $y_i$ is used for the mass or mol fraction of species $i$ in the vapor.↩︎

Chosen Symbol	Description	F & R	SVN	Ç & B	H & R
\(\alpha\)	Soave–Redlich–Kwong equation of state parameter, \(\alpha = [1+(0.48508+1.55171\omega-0.1561 \omega^2)(1+\sqrt{T_\mathrm{r}})]\)	\(\alpha\)	\(\alpha\)
\(\alpha\)	area covered per molecule adsorbed				\(\alpha\)
\(\beta\)	energy conversion function used in determination of the effectiveness factor for a nonisothermal catalyst pellet				\(\beta\)
\(\beta\)	volume expansivity
\(\gamma\)	activity coefficient				\(\gamma\)
\(\gamma\)	ratio of heat capacities, \(\gamma \equiv C_p/C_v\)		\(\gamma\)	\(k\)
\(\gamma_i\)	activity coefficient of species \(i\) in solution
\(\delta\)	volumetric expansion parameter				\(\delta_\mathrm{A}\)
\(\Delta\)	difference, e.g., \(out-in\) or \(final-initial\)	\(\Delta\)	\(\Delta\)	\(\Delta\)	\(\Delta\)
\(\epsilon_B\)	bed porosity				\(\epsilon_B\)
\(\epsilon_p\)	porosity of pellet or particle				\(\epsilon_p\)
\(\epsilon_\mathrm{total}\)	total porosity of packed bed				\(\epsilon_\mathrm{total}\)
\(\epsilon\)	emissivity of solid				\(\epsilon\)
\(\eta\)	catalyst effectiveness factor				\(\eta\)
\(\eta\)	thermal efficiency
\(\theta_i\)	fraction of catalyst surface covered by species i				\(\theta_i\)
\(\theta_v\)	fraction of surface sites that are vacant				\(\theta_v\)
\(\lambda\)	mean free path				\(\lambda\)
\(\mu\)	true mean or population mean (statistics)
\(\mu\)	dynamic viscosity, e.g, \(\mathrm{Pa}\cdot\mathrm{s}\)				\(\mu\)
\(\mu_i\)	chemical potential of species \(i\)				\(\mu_i\)
\(\nu\)	kinematic viscosity, e.g., \(\mathrm{m^2/s}\)				\(\nu\)
\(\nu_\mathrm{A}\)	stoichiometric coefficient for species \(\mathrm{A}\), e.g., \(\nu_{\mathrm{CO_2}}\)	\(\nu_\mathrm{A}\)	\(\nu_\mathrm{A}\)		\(\nu_\mathrm{A}\)
\(\nu_i\)	stoichiometric coefficient for unspecified species \(i\)	\(\nu_i\)	\(\nu_i\)		\(\nu_i\)
\(\xi\)	extent of reaction, reaction coordinate	\(\xi\)	\(\epsilon\)		\(\xi\)
\(\dot{\xi}\)	extent of reaction rate	\(\dot{\xi}\)	\(\dot{\epsilon}\)
\(\displaystyle\prod_i\)	product of the \(i\) terms that follow				\(\displaystyle\prod_i\)
\(\rho\)	density or mass concentration	\(\rho\)		\(\rho_\mathrm{A}\)	mass concentration of species A
\(\rho_B\)	bulk density of catalyst				\(\rho_B\)
\(\sigma\)	true or population standard deviation (statistics)
\(\sigma^2\)	true or population variance (statistics)
\(\sigma\)	surface tension		$
\(\sigma\)	surface site				\(\sigma\)
\(\sigma^2\)	variance of residence-time distribution curve				\(\sigma^2\)
\(\Pi\)	number of equilibrium phases	\(\Pi\)	\(\pi\)
\(\displaystyle\sum_i\)	sum of the \(i\) terms that follow				\(\displaystyle\sum_i\)
\(\tau\)	reactor space time				\(\tau\)
\(\tau_i\)	space time for reactor \(i\)				\(\tau_i\)
\(\tau_{1/2}\)	reaction half-life				\(\tau_{1/2}\)
\(\tau'\)	tortuosity factor				τ′
\(\phi_i\)	fugacity coefficient for species \(i\)		\(\hat{\phi}_i\)		\((f/P)_i\)
\(\hat{\phi}_i\)	fugacity coefficient for species \(i\) in solution		\(\phi_i\)		\((f/P)_i\)
\(\phi^0,\ \phi^1\)	generalized compressibiliity-factor correlation functions		\(\phi^0,\ \phi^1\)
\(\phi_Ln\)	Thiele modulus for an infinite flat plate catalyst, \(n\)th order reaction
\(\phi_Sn\)	Thiele modulus for a spherical catalyst, \(n\)th order reaction
\(\omega\)	Pitzer acentric factor	\(\omega\)	\(\omega\)