metabolic.rates = function( mass.g, temperature.C=NULL ) {
# require mass (g), temperature.C (C)
# from Robinson et al. (1983)
# specific standard MR
# = smr
# = 0.067 M^(-0.24) * exp(0.051 * Temp.Celcius)
# (Temp.Celcius; M in grams, MR in ml O2/g/hr)
#
# Converting to more standard units:
# 1 ml O2 = 4.8 cal (from paper)
# and 1 W = 7537.2 kcal/yr
# 1 ml O2 / g / hr = 4.8 * 24 * 365 kcal / yr / kg
# = 4.8 * 24 * 365 / (7537.2 W) / kg
# = 5.57873 W / kg
# noting similarity to Arrehnius formulation:
# smr ~ A * exp( -Ea / (K * T) )
# where: Ea = energy of activation { kcal/mol or J/ mol }
# R = 1.985877534 × 10−3 kcal/mol (Gas constant) or kB if on per molecule basis
# kB = 1.3806488(13)×10−23 J/K
# T = temperature in Kelvin
# then,
# A ~ 0.067 * M^(-0.24) / 5.57873 { W / kg }
# Ea ~ -b2 * T.C * R (T.C +273.15)
if (is.null(temperature.C)) temperature.C=10
tmed = median( temperature.C, na.rm=T )
oo = which(!is.finite( temperature.C) )
if (length(oo)>0) temperature.C[oo] = tmed
N.avogadro = 6.0221412927 * 10^23 ## mol−1
kB = 1.380648813 * 10^-23 # Boltzman's constant J/K
# K = kB * N.avogadro # R or kB , here directly R = kB {J/K} * N.avogadro {n/mol} muiliplied to give units of J / K / mol
K = 8.314462175 # as above to greater precision
b0 = 0.067
b1 = -0.24
b2 = 0.051
from.ml.O2.per.g.per.hr.to.W.per.kg = 1 / 5.57873
# Arrhenius parameterization:
# the pre-factor -> total number of collisions ... ie. similar to encounter rate
A = b0 * (mass.g)^b1 * from.ml.O2.per.g.per.hr.to.W.per.kg
# 'activation energy'
Ea = b2 * temperature.C * K * ( temperature.C + 273.15 )
# fraction of collisions leading to a reaction (ie. a metabolic event -- e.g. dissipation) .. reacting or Pr of reaction -- incorporates (i.e., due to) temperature influence
Pr.Reaction = exp( -Ea / (K * (temperature.C + 273.15) ) ) ## == exp( b2 * temperature.C )
smr = A * Pr.Reaction # == b0 * (mass.g)^b1 * exp( b2 * temperature.C ) * from.ml.O2.per.g.per.hr.to.W.per.kg
mr = smr * mass.g
x = data.frame( smr=smr, mr=mr, Ea=Ea, A=A, Pr.Reaction=Pr.Reaction )
## units:
## smr,A ~ {W/kg};
## mr~{W};
## Ea ~ {J/mol} energy per per mol
return(x)
}
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