bomb calorimetry experiment derivation
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8/19/2019 Bomb Calorimetry Experiment Derivation
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For a batch process, the first law of thermodynamics states that,
∆ U =Q+W (1)
Using equation 1 for ∆ U cal and since it is an adiabatic calorimeter (Q=0) and the wor
e!erted by the stirrer is negligible (" =0),
∆ U cal=0 (#)
$he energy balance in the bomb%s case is
dE
dt =d ( v
2
2+gh+U )=dQ+dW (&)
'ssuming inetic and otential energy are relati*ely small
dU =dQ+dW (+)
ntegrating with "=0 since the bomb has a constant *olume (d-=0) ,
∆ U B=Q B (.)
For the ∆ U of the entire process,
∆ U total=∆ U system+∆ U surroundings (/)
which we can define the reactants (sample and o!ygen) to be the system and the rest of the
calorimeter (bomb and water) to be the surroundings
∆ U total is essentially ero gi*ing,
∆ U reactants=−∆ U calorimeter (2)
where ∆ U surroundings = 34*d$ from $1 to $#
$he temperature change is relati*ely small and it is usually *alid to consider 4 total to be constant5ote that the negati*e sign indicates a decrease in energy of the process path
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6y definition,
dH =dU reactants+d ( PV ) (7)
8ifferentiating d(-),
d ( PV )=VdP+ PdV (9)
'ssuming there is negligible e!pansion wor done,
dH =dU reactants+VdP (10)
$he products are then assumed to beha*e ideally to gi*e
d ( PV )=V d nRT
V (11)
d ( PV )= R d(nT ) (1#)
d ( PV )= R ( ndT +Tdn ) (1&)
at constant temperature, d$=0,
d ( PV )= RTdn
(1+)
:ubstituting equation 10 to 2 and integrating,
∫dH =∫dU +∫ RTdn (1.)
∆Ho = ∆Ureactants + RT∆n (16)
where ∆Ho is the standard enthalpy change, ∆U is the standard internal energy change, R is the
universal gas constant, T is the standard teperature and ∆n is the change in the nu!er o"
oles during the process#
$o determine the 4bomb which is constant for both samples,
C bomb dT =C total dT −C water dT (12)
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C bomb=∆ U B−mwater C water ∆ T
∆ T (17)
C bomb=Qba mba+5857.59(m0−m)
∆ T
−mwater C water (19)
where 4bomb is the heat capacity of the calorimeter, Qba is the heat liberated by the actual
combustion of benoic acid, mba is the mass of the sample, m 0 is the initial mass of the wire and
m is the mass of the wire after ignition, mwater is the mass of water, 4water is the heat capacity of
water and ;$ is the change in temperature of water during the combustion process