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General Physical Chemistry I Lecture 6 Aleksey Kocherzhenko February 24, 2015" Thermodynamics" the capacity to do work" Ø The branch of science that studies transformations of energy, in particular, the transformation of heat into work and vice versa" We will learn to quantify heat shortly" Mechanical work performed by a force:" Elementary work" dA = F~ · d~l Elementary displacement" Energy conservation:" Force" Energy can be neither created nor destroyed, but only converted from one form into another or moved from place to place" Ø Energy is released or absorbed in most chemical reactions" Ø Thermodynamics identifies chemical reactions that may or may not occur and the equilibrium of these chemical reactions" A thermodynamic system is (any) part of the universe that we are currently interested in studying" The surroundings is a much larger part of the universe that the system may interact with " Ø We assume that when a system interacts with its surroundings, the state of the system changes, but the state of the surroundings does not (e.g., constant T )" The first law of thermodynamics" Open, closed, and isolated systems" Open system: can exchange both particles and energy with its surroundings " Closed system: contains a constant number of particles, but can exchange energy with its surroundings " Isolated system: can exchange neither particles, nor energy with its surroundings " If:" Processes in a closed system:" ⌫ p = const à isobaric" V = const à isochoric" “iso” = “same”" T = const à isothermal" For perfect gas only:" = const ) pV = const ) ) V T p T = const = const Heat and work" Ø Heat – energy transferred as a result of temperature difference" @ high T, molecules move faster" à part of their energy can be transferred to slower molecules in collisions" ~ ):" Ø Work (performed by force F F~ ↵ d~l dA = F~ · d~l Displacement of object on which the work is performed" Force performing the work" ~ Scalar product:" F · d~l = F~ d~l cos ↵ pS F~ ? d~l ) dA = 0 F~ k d~l ) dA = dAmax Ø Can a gas perform work?" à Yes, by expansion " m Ø Forces acting on piston – ?" à In equilibrium," pext S + mg = pint S How can we make the gas expand and move the piston? " S mg pext S Cylinder with piston" Expansion work" pS dl :" gas volume changes by" dV = Sdl If dl is very small à tiny volume change" ) p ⇡ const Piston moves by S m mg pext S Work performed on piston by gas:" dA = pS dl = pdV |{z} =F By convention, work performed on system is positive (system gains energy): "dA = pdV Work performed by system is negative (system uses energy):" dA Perfect gas law:" pV = ⌫RT à changing = pdV ⌫ and/or T changes p and/or V " Change amount of gas:" Zn (s) + 2HCl (aq) ! ZnCl2 (aq) + H2 (g) (or, just pump gas into the cylinder)" External pressure and weight of piston are constant "à if conditions of gas inside cylinder change, it may expand/compress " until pext S + mg = pint S holds again" Maximum expansion work" pS Imagine that there is no external pressure:" S weightless piston," m pext = 0 =0 A single molecule could send the piston flying off to infinity!" Ø Gas could expand without performing work!" pext S Ø Work is only performed if there is an opposing force (in reality, there always is)" Gas will, obviously, not expand if "pext >p à maximum expansion work for pext = p at all stages of the expansion (maximum possible opposing force) " à equivalent to saying that the piston is at equilibrium at all stages of the expansion (forces are balanced: pext S = pS )" A system that remains in mechanical equilibrium with its surroundings at all stages of the expansion performs maximum expansion work" If pext = p, expansion/compression can be reversed by an infinitesimal change in pressure: such a process is called reversible " Work performed in isothermal expansion" Expansion at constant temperature:" T = const Assume that the external pressure balances the pressure of the gas inside the cylinder at all times:" pext = p Elementary work:" dA = pdV Total work performed" in expansion from Vi to Vf :" A= pS S m=0 pext S Z Vf pdV Vi ⌫RT Perfect gas law:" pV = ⌫RT ) p = V Z Vf dV Vf > 0 if "Vf > Vi ) A = ⌫RT = ⌫RT ln V Vi (expansion)" Vi Isothermal process, temperature is constant" Expansion work is negative" Path-dependence of work" Isothermal expansion" Another way of getting from Vi to V "f First, cool the gas at constant volume" (no expansion à no work performed)" Then, let it expand as you heat it at constant pressure" pf We calculated:" For this process:" Vf ⌫RT ln Vi A=0 The work doesn’t just depend on the initial and final states of the system, but also on how the system gets from one to the other" = A= Z Vf pf dV = Vi pf (Vf Vi ) The internal energy" Internal energy of a system = sum of all the kinetic and potential contributions to the energy of all the atoms, ions, and molecules in the system" Ø The origin for energy can be selected arbitrarily, so we are only concerned with energy differences, not energy values as such" Ø The change in the internal energy of a system: " dU = dA + dq Work performed on the system (positive) Heat transferred" or by the system (negative) " to the system (positive) or from the Ø Isothermal expansion of a perfect gas:" system to the surroundings (negative)" ü No interactions between atoms à potential energy = 0" à Internal energy = kinetic energy" Kinetic definition of temperature" 2Ek T = 3kB There is one-to-one correspondence between T and Ek!" à No change in temperature = = no change in kinetic energy = no change in internal energy" à In an isothermal process, "T = const ) dU = 0 ) dq = dA The first law of thermodynamics" The change in the internal energy of a system: "dU = dA + dq Work performed on the system (positive) Heat transferred" or by the system (negative) " to the system (positive) or from the The first law of thermodynamics" system to the surroundings (negative)" Verbal statement: The " change in the internal energy of the system is the sum of the heat transferred to the system and the work performed on it" An isolated system does not exchange energy with its surroundings, neither as heat, nor as work: dq " = dA = 0 ) dU = 0 The first law of thermodynamics is the law of energy conservation: energy can be converted from one form to another, but it cannot be created or destroyed" à Perpetual motion machines that perform more work than they use energy cannot be created" Internal energy as a state function" The internal energy only depends on the initial and final state of the system (not on how it transferred from one to the other)" Ø Quantities like that are referred to as state functions" Ø Work is not a state function: as we have seen, it depends on the path by which the system got from the initial to the final state " Enthalpy" Many processes, particularly chemical reactions, occur at constant pressure (in open vessels), not at constant volume" à Transferred heat ≠ change in internal energy" Ø Heat transfer in such processes is conveniently characterized in terms of the enthalpy, defined as:" H = U + pV Positive for endothermic reactions " At constant pressure:" dH = dU + pdV Negative for exothermic reactions" At constant pressure, the heat transferred to the system is equal to the change in enthalpy " Ø The enthalpy is defined in terms of state functions only ( U, and thus it is itself a state function" p, V ), Ø Like the internal energy, the enthalpy is an extensive quantity: it depends on the amount of substance, and molar enthalpy can be defined"