Atkins’ Physical Chemistry Eighth Edition Chapter 2 The First Law Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio de Paula.

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