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

Homework Set #2 Atkins & de Paula, 8e Chap 2 Exercises: all part (b) unless noted 2, 3, 4, 7, 8, 12, 13, 15 19, 21, 23, 25

Fig 2.1 Types of Systems

Fig 2.2 Comparison of Adiabatic and Diathermic Systems for Exo- and Endothermic Processes

Fig 2.3 Thermal energy from system to surroundings

Fig 2.4 System does work on surroundings

Equivalent Expressions of the First Law: Conservation of energy In terms of heat and work Formal statement

Internal Energy Internal energy, U, is the total kinetic and potential energy of the molecules in the system Approximated by the equipartition theorem: Each degree of freedom contributes ½ kT to U Degrees of freedom are associated with: translation, rotation, and vibration

Kinetic Energy of Translational motion: According to the equipartition theorem, the mean trans energy for one molecule is 3/2 kT E K = 3/2 RT for one mole of molecules ∴ U m = U m (0) + 3/2 RT where U m (0) ≡ molar internal energy at T = 0

Fig 2.5 Rotational modes of molecules and corresponding average energies at temperature T Linear Nonlinear U m = U m (0) + 5/2 RT U m = U m (0) + 3 RT

First Law in terms of conservation of energy: The internal energy of an isolated system is constant No ‘perpetual motion machine’ can exist

Waterfall by M.C. Escher

First Law in terms of conservation of energy: The internal energy of an isolated system is constant No ‘perpetual motion machine’ can exist First Law in terms of heat and work: ΔU = q + w (Internal energy is a state function) i.e., heat and work are equivalent ways of changing U

Illustration of change in internal energy, ΔU, as a state function. The work needed to change an adiabatic system from one state to another is the same however the work is done. Formal Statement of First Law:

Fig 2.6 General expansion work Focus on infinitesimal changes ΔU = q + w becomes dU = dq + dw When gas expands:

Fig 2.7 Work done by a gas when it expands against a constant external pressure Irreversible expansion

Fig 2.8 Work done by a gas when it expands isothermally against a non-constant external pressure. Set P ex = P at each step of expansion System always at equilibrium Since P ex is not constant, it can’t be brought out Reversible expansion

Isothermal reversible expansion Since P ex is not constant, it can’t be brought out However, P ex depends on V, so substitute using PV = nRT