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

Heat transactions In general: dU = dq + dw exp + dw e where dw e ≡ extra work in addition to expansion At ΔV = 0 and no additional work:dU = dq V For a measurable change: ΔU = q V Implies that ΔU can be obtained from measurement of heat Bomb calorimeter used to determine q V 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:

Change in internal energy as a function of temperature and volume U(T,V), so we hold one variable (V) constant, and take the ‘partial derivative’ with respect to the other (T). Fig 2.11

Fig 2.12 At constant volume: dU = dq If system can change volume, dU ≠ dq Some heat into the system is converted to work ∴ dU < dq Constant pressure processes much more common than constant volume processes

If C V is assumed to be constant with temperature for macroscopic changes: ΔU = C V ΔT or: q V = C V ΔT Enthalpy ≡ heat flow under constant pressure H ≡ U + PV ΔH = ΔU + PΔV ΔH = ΔU + Δn g RT

Fig 2.14 Plot of enthalpy as a function of temperature C P = (∂H/∂T) P The heat capacity at constant pressure: C p > C v C V = (∂U/∂T) V C p – C v = nR

Variation of enthalpy with temperature If C P is assumed to be constant with temperature for macroscopic changes: ΔH = C P ΔT or: q P = C P ΔT If ΔT ≥ 50 o C, use empirical expression, e.g.: with empirical parameters from Table 2.2

Fig 2.17 Consider change of state: T i, V i → T f, V f Internal energy is a state function ∴ change can be considered in two steps Adiabatic Changes

Fig 2.17 Variation of temperature as a perfect gas is expanded reversibly and adiabatically: where:

Fig 2.18 (a) Variation of pressure with volume in a reversible adiabatic expansion where the heat capacity ratio:

Fig 2.18 (b) Pressure declines more steeply for an adiabat than for an isotherm Temperature decreases in an adiabatic expansion