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Atkins’ Physical ChemistryEighth Edition
Chapter 2The First Law
Copyright © 2006 by Peter Atkins and Julio de Paula
Peter Atkins • Julio de Paula
Heat transactions
In general: dU = dq + dwexp + dwe
where dwe ≡ extra work in addition to expansion
At ΔV = 0 and no additional work: dU = dqV
For a measurable change: ΔU = qV
• Implies that ΔU can be obtained from measurement of heat
• Bomb calorimeter used to determine qV and, hence, ΔU
Fig 2.9
Constant-volume
bomb calorimeter
Fig 2.10 Change in internal energy as function of temperature
Slope = (∂U/∂T)V
The heat capacity
at
constant volume:
VV T
UC
Change in internal energyas a function of temperature
and volume
• U(T,V), so we hold one variable (V) constant,
and take the ‘partial derivative’ with respectto the other (T).
Fig 2.11
VV T
UC
δ
δ
Fig 2.12
At constant volume: dU = dq
If system can change volume,
dU ≠ dq
• Some heat into the systemis converted to work
• ∴ dU < dq
• Constant pressure processes much more common than constant volume processes
If CV is assumed to be constant with temperature for macroscopic changes:
ΔU = CV ΔT
or: qV = CV ΔT
Enthalpy ≡ heat flow under constant pressure
H ≡ U + PV
ΔH = ΔU + PΔV
ΔH = ΔU + ΔngRT
Fig 2.14
Plot of enthalpy as a
function of temperature
CP = (∂H/∂T)PThe heat capacity
atconstant pressure:
PP T
HC
Cp > CvCV = (∂U/∂T)V
Cp – Cv = nR
Variation of enthalpy with temperature
PP T
HC
If CP is assumed to be constant with temperature for macroscopic changes:
ΔH = CP ΔT
or: qP = CP ΔT
If ΔT ≥ 50 oC, use empirical expression, e.g.:
2m,PT
cbTaC with empirical parameters from
Table 2.2
Fig 2.17
• Consider change of state:
Ti, Vi → Tf, Vf
• Internal energy is a
state function
∴ change can be
considered in two steps
Adiabatic Changes
Fig 2.17Variation of temperatureas a perfect gas is
expanded reversiblyand adiabatically:
R
Cc mV ,
cii
cff TVTV
where:
Fig 2.18 (a) Variation of pressure with volume in a reversible adiabatic expansion
γγiiff VPVP
m,V
m,P
C
Cγ
where the heat capacity ratio:
Fig 2.18 (b)
• Pressure declines more steeply for an adiabatthan for an isotherm
• Temperature decreases
in an adiabatic expansion