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CHEM 11132 Thermodynamics Textbooks P. W. Atkins The Elements of Physical Chemistry (Third Ed., Ch. 10) P. W. Atkins Physical Chemistry Any Physical Chemistry Text Book; Levine, Daniel & Alberty, Barrow. Thermodynamics • Thermodynamics is the branch of physical chemistry that provides a macroscopic description of systems at chemical equilibrium, based on energy transformations. [Thermodynamics: The science of energy] • A macroscopic description is based on the properties of bulk matter rather than individual atoms and molecules. • A microscopic description deals with the atomic and molecular level, as in quantum mechanics. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Approaches to studying thermodynamics – Macroscopic (Classical thermodynamics) • study large number of particles (molecules) that make up the substance in question • does not require knowledge of the behavior of individual molecules – Microscopic (Statistical thermodynamics) • concerned within behavior of individual particles (molecules) • study average behavior of large groups of individual particles INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE What is Energy? Energy is the capacity to do work Energy is the capacity to do work • Radiant energy comes from the sun and is earth‟s primary energy source • Thermal energy is the energy associated with the random motion of atoms and molecules • Chemical energy is the energy stored within the bonds of chemical substances • Nuclear energy is the energy stored within the collection of neutrons and protons in the atom • Potential energy is the energy available by virtue of an object‟s position Energy Changes in Chemical Reactions Heat is the transfer of thermal energy between two bodies that are at different temperatures. Temperature is a measure of the thermal energy. Temperature = Thermal Energy 900C 400C Thermochemistry is the study of heat change in chemical reactions. Systems & Surroundings In thermodynamics, the world is divided into a system and its surroundings A system is the part of the world we want to study (e.g. a reaction mixture in a flask) The surroundings consist of everything else outside the system System and Surroundings System - the part of the world, with defined boundaries, in which we have a special interest. Surroundings - The area outside the system. The surroundings are separated from the system by boundaries.. Boundary - real or imaginary layer that separates the system from its surroundings system surroundings Changes in a system are associated with the transfer of energy Unstable: falling or rolling Stable: at rest in lowest energy state Metastable: in low-energy perch Natural systems tend toward states of minimum energy SYSTEM OPEN ISOLATED CLOSED Types of Systems Open - exchanges matter and energy with surroundings. Closed - exchanges only energy with surroundings. Isolated - no interchange with surroundings. Matter Energy Energy open Exchange: mass & energy closed isolated energy nothing Getting Started All of thermodynamics can be expressed in terms of four quantities Temperature (T) Internal Energy (U) Entropy (S) Heat (Q) These quantities will be defined as we progress through the lesson INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Properties Any characteristic of a system in equilibrium is called a property. Intensive property are independent of the amount of material present: e.g. Density (D), Pressure (P), Temperature(T) Extensive property are dependent on the amount of material present: e.g. Volume (V), Mass (m), Total energy INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE State & Equilibrium State of a system • system that is not undergoing any change • all properties of system are known & are not changing • if one property changes then the state of the system changes Thermodynamic equilibrium • “equilibrium” - state of balance • A system is in equilibrium if it maintains thermal (uniform temperature), mechanical (uniform pressure), phase (mass of two phases), and chemical equilibrium INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Processes & Paths Process • when a system changes from one equilibrium state to another one • some special processes: • isobaric process - constant pressure process • isothermal process - constant temperature process Path • series of states which a system passes through during a process INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Compression Process DV = Vfinal - Vinitial INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. energy, pressure, volume, temperature DE = Efinal - Einitial DP = Pfinal - Pinitial DV = Vfinal - Vinitial DT = Tfinal - Tinitial Potential energy of hiker 1 and hiker 2 is the same even though they took different paths. Exothermic process is any process that gives off heat – transfers thermal energy from the system to the surroundings. 2H2 (g) + O2 (g) H2O (g) 2H2O (l) + energy H2O (l) + energy Endothermic process is any process in which heat has to be supplied to the system from the surroundings. energy + 2HgO (s) energy + H2O (s) 2Hg (l) + O2 (g) H2O (l) Exothermic process – to its surroundings Endothermic process – to its surroundings 24 Direction of heat flow Sign Reaction Type Heat flows OUT of the system Negative – “Losing heat” Exothermic Heat flows INTO the system Positive + “Gaining heat” Endothermic © 2009 Brooks/Cole - Cengage ΔH - change in heat content for a reaction at constant pressure. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Enthalpy (H) is used to quantify the heat flow into or out of a system in a process that occurs at constant pressure. DH = H (products) – H (reactants) DH = heat given off or absorbed during a reaction at constant pressure Hproducts > Hreactants DH > 0 Hproducts < Hreactants DH < 0 Thermodynamics States - state variables A state variable describes the state of a system at time t, but it does not reveal how the system was put into that state. Examples of state variables: • P = pressure (Pa or N/m2), • T = temperature (K), • V = volume (m3), • n = number of moles, and • U = internal energy (J). INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Temperature is a measure of the thermal energy. Temperature = Thermal Energy Heat, q, is energy in transit as a result of a temperature difference. Temperature, T is an intensive property that is used to define the state of a system and determines the direction in which energy flows as heat. Diathermic Walls that permit the passage of energy as heat are called diathermic. Eg. Metal container INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Adiabatic Walls that do not permit heat to pass through even though there is a difference in temperature are called adiabatic*. Eg. Wall of a vacuum flask (*from the Greek word for „not passing through‟) INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Internal energy (U) Internal energy is defined as the energy associated with the random, disordered motion of molecules. The internal energy is the total energy contained in a thermodynamic system. Internal energy has two major components, kinetic energy and potential energy. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE The internal energy is the grand total energy of the system. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE UNITS OF ENERGY S.I. unit of energy is the joule (J) Heat and work ( energy in transit) also measured in joules 1 kJ (kilojoule) = 103 J Calorie (cal): 1 cal is the energy needed to raise the temperature of 1g of water by 1oC 1 cal = 4.184 J Energy Kinetic energy (EK) Energy due to motion Potential energy (EP) Energy due to position (stored energy) Total Energy = Kinetic Energy + E EP = EK + Potential Energy Kinetic energy & potential energy are interchangeable Ball thrown upwards slows & loses kinetic energy but gains potential energy The reverse happens as it falls back to the ground Energy and Its Conservation Energy cannot be created or destroyed; it can only change forms First law of thermodynamics – energy can be converted from one form to another, but cannot be created or destroyed. DEsystem + DEsurroundings = 0 or DEsystem = -DEsurroundings C3H8 + 5O2 Conservation of energy 3CO2 + 4H2O Exothermic chemical reaction! Chemical energy lost by combustion = Energy gained by the surroundings system surroundings In chemistry, we are normally interested in the energy changes associated with the system, not with its surroundings. Therefore, a more useful form of the first law is: (for DEsystem) DE = q + w q is the heat exchange between the system and the surroundings w is the work done on (or by) the system w = -PDV when a gas expands against a constant external pressure Internal Energy ΔU = Q + W Heat Energy (Conservation of Energy) Work Done Work and Heat Example: an example of energy leaving a system as work INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE System did work in pushing the piston upward Dx W = Fd = (PA)∆x W =-Pex ∆V INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Work work can be defined as force F multiplied by distance d : System did work in pushing the piston upward W = Fd = (PA)∆x W =-Pex ∆V {const. external press.} INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Work Done On the System w=Fxd w = -P DV DV > 0 -PDV < 0 wsys < 0 Work is not a state function! Dw = wfinal - winitial initial final A sample of nitrogen gas expands in volume from 1.6 L to 5.4 L at constant temperature. What is the work done in joules if the gas expands (a) against a vacuum and (b) against a constant pressure of 3.7 atm? w = -Pex DV (a) DV = 5.4 L – 1.6 L = 3.8 L P = 0 atm W = -0 atm x 3.8 L = 0 L•atm = 0 joules (b) DV = 5.4 L – 1.6 L = 3.8 L P = 3.7 atm w = -3.7 atm x 3.8 L = -14.1 L•atm 101.3 J = -1430 J w = -14.1 L•atm x 1L•atm Practice Exercise INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Work done by an expanding gas, constant pressure: Isobaric If the volume stays constant, nothing moves and no work is done. Isochoric Reversible and irreversible processes maximum work w = -Pex DV Maximum work is obtained when the external pressure is only infinitesimally less than the pressure of the gas in the system. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE A process that can be reversed by an infinitesimal change in a variable—in this case, the pressure—is said to be reversible. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE In contrast, an expansion against a fixed external pressure Proceeds at a finite rate until the internal and external Pressures are equalized. Irreversible process Spontaneous processes are inheretantly irreversible. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Reversible processes • • • infinitely slow at equilibrium do maximum work Irreversible processes (spontaneous) • • • go at finite rate Not at equilibrium do less than the maximum work Reversible processes are also called equilibrium processes INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE The work of reversible isothermal expansion If the temperature is constant, the pressure varies inversely with the volume. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE For a gas to expand reversibly, the external pressure must be adjusted to match the internal pressure at each stage of the expansion INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE FOUR THERMODYNAMIC PROCESSES: • Isochoric Process: DV = 0 • Isobaric Process: DP = 0 • Isothermal Process: DT = 0 • Adiabatic Process: INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE DQ = 0 ADIABATIC PROCESS: NO HEAT EXCHANGE, D Q = 0 DU Work Out DQ = 0 +DU Work In Work done at EXPENSE of internal energy INPUT Work INCREASES internal energy INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE ADIABATIC EXAMPLE: PA A B PB V1 Insulated Walls: DQ = 0 INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE V2 Expanding gas does work with zero heat loss. Work = -DU The measurement of heat Temperature is a measure of the thermal energy. When a substance is heated, its temperature typically rises. Heating Curves INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE The measurement of heat reaction reaction Exothermic reaction, heat given off & temperature of water rises Endothermic reaction, heat taken in & temperature of water drops Heat ↔ Temperature For a specified energy, q, transferred by heating, the size of the resulting temperature change, ΔT, depends on the „heat capacity‟ of the substance. The heat capacity, C, is defined as: J K-1 Heat ↔ INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Temperature Extensive property (a property that depends on the amount of substance in the sample) 2 kg of iron has twice the heat capacity of 1 kg of iron, so twice as much heat is required to raise its temperature by a given amount. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE A brief illustration If the heat capacity of a beaker of water is 0.50 kJ K-1, and we observe a temperature rise of 4.0 K, then we can infer that the heat transferred to the water is: INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE It is more convenient to report the heat capacity of a substance as an intensive property (a property that is independent of the amount of substance in the sample). specific heat capacity, Cs, molar heat capacity,Cm, INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Cs = C / m J K-1 g-1 Cm = C / n J K-1 mol-1 Differential forms So far we have written the First Law as, ΔU = Q + W where the Δ implies a finite change in U. We could just as well have written it for an infinitesimal change in U, using the language of calculus: INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE w = -Pex DV if this is the only kind of work done, the First Law can be written {pV work only} Work due to gas expansions is sometimes called "pV work". INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Unless we say otherwise, we will assume that the only kind of work done is that due to gas expansions, and so use the form of the First Law as: INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Constant volume processes If we imagine a process taking place in a sealed container, at constant volume, then no work can be done as the gas cannot expand 0 {constant volume} INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE If we want to measure ΔU ……………? all we have to do is measure the heat change under constant volume conditions. Heat capacities (re-visit) For infinitesimal quantities this relationship becomes INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE For chemical substances it is convenient to use the molar heat capacity, Cm, which is the amount of heat needed to raise one mole of the substance through one degree. Cm = C / n m INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE J K-1 mol-1 For a process taking place at constant volume, ,m where CV,m is the molar heat capacity at constant volume. Writing this in the differential form, ,m INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE {constant volume} where we are now assuming that dU is the change in internal energy per mole (i.e. n = 1). Mathematically, this can be expressed as a partial derivative: {definition of CV,m} INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Constant pressure processes – enthalpy Processes taking place under constant pressure conditions are more common, especially in chemistry, where open apparatus "on the bench" can be considered to be at constant pressure. If we heat a gas at constant external pressure it will expand and by doing so it will do work INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE For a given amount of heat, the increase in the internal energy will be less in a constant pressure process than in a constant volume one on account of part of the heat being converted to work. It will be convenient to have a state function whose value is equal to this heat supplied at constant pressure; Enthalpy (H) ~ heat content (q) @ constant pressure INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE The function we need is called the enthalpy, H and it is defined as INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE 86 Properties of Enthalpy • Since P, and V are all state functions, enthalpy H must be a state function also. • Enthalpy changes have unique values. DH = qP Enthalpy change depends only on the initial and final states. • Enthalpy is an extensive property. – It depends on how much of the substance is present. Prentice Hall © 2005 Two logs on a fire give off twice as much heat as does one log. Chapter Six Enthalpy change (dH) INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Enthalpy change (dH) (p + dp) (V + dV) (U + dU) As a result of the changes in p, V and U, it is clear that H will also change by a small amount, dH (H + dH) INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Multiplying this out gives INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE from the First Law Now we substitute in the First Law, in the form of the expression for dU, INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Finally, we impose the condition of constant external pressure, Heat change measured under conditions of constant pressure. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Constant-Pressure Calorimetry Coffee-cup calorimeter INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Heat capacity at constant pressure {constant pressure} where Cp is the constant pressure molar heat capacity. {definition of Cp,m} INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Variation of enthalpy with temperature Suppose we know the (molar) enthalpy, H(T1), of a substance at a particular temperature, T1, but we want to know its (molar) enthalpy, H(T2), at another temperature T2. Heat capacities are the key to finding how H varies with T. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Heat capacities are the key to finding how H varies with T. rearrange this to give {constant pressure} Both sides of the Eq. can be integrated. First the left-hand side INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Both sides of the Eq. can be integrated. First the left-hand side The right-hand side of Eq. is also integrated, and we make the additional assumption that Cp does not vary with temperature, INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Putting the left- and right-hand sides together we have This is a practical relationship: if we know H at one temperature and the heat capacity, we can work out H at any other temperature (assuming that it is valid to consider Cp as constant in this range). INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Second law of thermodynamics Second Law: The entropy of the Universe increases in a spontaneous process. Spontaneity Reaction will occur ―naturally‖ INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Spontaneous Physical and Chemical Processes • A waterfall runs downhill • A lump of sugar dissolves in a cup of coffee • At 1 atm, water freezes below 0 0C and ice melts above 0 0C • Heat flows from a hotter object to a colder object • A gas expands in an evacuated bulb • Iron exposed to oxygen and water forms rust spontaneous nonspontaneous spontaneous nonspontaneous The Second Law states that the entropy of the Universe must increase in a spontaneous process. Entropy (S) is a measure of the randomness or disorder of a system. The entropy change of the Universe can then be calculated from INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Entropy (S) is a measure of the randomness or disorder of a system. More ordered Less random INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Less ordered More random Solids Highly ordered ⇒ low entropy Liquids Less ordered ⇒ medium entropy Gases Highly disordered ⇒ high entropy INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Entropy State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. energy, enthalpy, pressure, volume, temperature , entropy Potential energy of hiker 1 and hiker 2 is the same even though they took different paths. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE We saw that the entropy of a substance increases as it is heated. Formally, entropy is defined as INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE The direction of spontaneous change The apparent driving force of spontaneous change is the tendency of energy and matter to become disordered. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Dispersal of matter Dispersal of energy INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE In summary, we have identified two basic types of spontaneous physical process: 1. Matter tends to become disordered. 2. Energy tends to become disordered. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE 2nd Law of Thermodynamics 113 A reaction is spontaneous if ∆S for the universe is positive. ∆Suniverse = ∆Ssystem + ∆Ssurroundings ∆Suniverse > 0 for spontaneous process First calc. entropy created by matter dispersal (∆Ssystem) Next, calc. entropy created by energy dispersal (∆Ssurround) Entropy change of the system INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Entropy change of the surroundings Now, the heat that the surroundings absorbs comes from the system so: INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Entropy change of the Universe INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Measuring entropy Entropies can be evaluated from measurements of heat capacities in the following way. The definition of entropy is, in differential form a process at constant pressure, INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Next we use the definition of the constant pressure heat capacity to express dH in terms of Cp : Substituting this into above Eq. gives {const. pressure} INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE To find the entropy at temperature T* both sides are integrated from T = 0 up to T* Measuring heat capacities right down to absolute zero is not a particularly easy task.The entropy values determined in this way are called absolute entropies. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Converting entropies from one temperature to another It will therefore be convenient to have a way of converting the value of the entropy from one temperature to another, just as we did for enthalpies INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE This is a practical relationship for converting entropies from one temperature to another. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Second law states: • Entropy of the Universe must increase in a spontaneous process DSuniv 0 spontaneou s DSuniv 0 equilibrium INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE The spontaneity of chemical reactions Do we have to keep calculating ∆Suniv ? Not necessarily! A convenient way of using second law…… INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE at constant pressure, INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Multiplying through by –T , we obtain INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Gibbs Free Energy The Gibbs Free Energy is a new state function, defined as: G H TS Sometimes the Gibbs energy is called "the Gibbs free energy", "the Gibbs function "or simply "the free energy". INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Josiah Willard Gibbs (1839-1903) At constant T and P, consideration of ∆G will answer the question ―Will a given reaction be spontaneous?‖ DG < 0 DG > 0 DG = 0 process is spontaneous reverse process is spontaneous Equilibrium The Gibbs Free Energy is a direct measure of spontaneity INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE Starting from the definition of G, we can form the complete differential as we did before, Now, we consider a process at constant temperature, so that the SdT term is zero. DG DH TDS INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE DrH = H (products) – H (reactants) INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE ΔrS and ΔrG are defined in the same way: INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE The Master Equations We are almost in a position to derive the key relationship between the standard Gibbs energy change and the equilibrium constant: A key idea in thermodynamics is that of a standard state. The standard state of a substance is the pure form at a pressure of one bar and at the specified temperature INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE where INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE The Third Law of Thermodynamics Entropy is related to the dispersal of energy (degree of randomness) of a substance. Entropy is directly proportional to the absolute temperature. Cooling the system decreases the disorder. At a very low temperature, the disorder decreases to 0 (i.e., 0 J/(K mole) value for S). The most ordered arrangement of any substance is a perfect crystal! INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE The Third Law of Thermodynamics The entropy of any perfect crystal is 0 J /(K mole) at 0 K (absolute 0!) Due to the Third Law, we are able to calculate absolute entropy values. INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE The Zeroth Law of Thermodynamics INTERNATIONAL FOOD POLICY RESEARCH INSTITUTE