Chapter 2. First Law of thermodynamics Important Topics You should review • First law of thermodynamics • Law of Conservation of Energy • Work, heat and internal energy • Heat Capacity Cv, Cp • Expansion work • Standard State • Heat capacity • Newton, Joule units • Reversible and irreversible process • Enthalpy • Math • Isothermal & adiabatic changes • Vectors • Joule-Thomson expansion • Scalar products •Thermochemistry • Properties of ln System and environment • System The part of world we want to describe thermodynamically e.g. matter, reaction vessel, engine; completely enclosed within a well-defined boundary. • Anything outside of the system are the surroundings. Type of system Universe surroundings Open system Closed system Isolated system system wall wall can be either diathermic (heat can flow) or adiabatic (insulating). Open for Closed for Closed both matter but for both matter open for matter and energy and energy energy Processes • Process: What is done to or by the system to cause a change of state (gas expansion, heating, mixing, reaction) • Isothermal process: the temperature does not change • Adiabatic process: no heat enters or leaves system; q = 0 PHYSICAL CHEMISTRY: QUANTA, MATTER, AND CHANGE 2E| PETER ATKINS| JULIO DE PAULA | RONALD FRIEDMAN ©2014 W. H. FREEMAN D COMPANY Work Work is associated with a thermodynamic process. Transfer of Energy Some kinds of work: Example: 1. mechanical work compression of spring, turn of shaft 2. electrical work charging of battery 3. magnetic work magnetizing a system 4. gravitational work raising of a weight Will concentrate on special case of mechanical work called PV work. (arises from compression/expansion) x2 Mechanical work is defined as w F(x)dx work = force x displacement in direction of force x1 Sign convention work done on system, heat supplied to system : + work done by system, heat removed from system : - Internal Energy • State: Described when we specify values for enough intensive variables such that all additional properties are fixed • State Function: Physical property that has a specific value once the state is defined e.g. Volume V(T, P); independent of path (i.e. how we got to that state) • Path function: a property of a system that depends on the previous history of the current state of the system. (heat, work) • Internal Energy: State variable, U Don't confuse with potential E or intermolecular potential Total energy of system • Only changes in energy, U, are calculable final initial First law of thermodynamics (Conservation of Energy) • The total amount of energy is the universe is constant. • Energy may be neither created nor destroyed, but it may be converted from one form to another. U U2 U1 q w q: heat; w: work dU = dw + dq • Change in U is the sum of the heat and work supplied to a system in going from state 1 to state 2 • Energy is conserved only for system + surroundings; system & surroundings can exchange energy • In terms of the operation of machines, it is impossible to construct a device which will work continuously without the input of energy to the device. • The best that you can do is break even; you can't win. PV Work x2 Gas expanding against a piston w Fdx (- sign b/c work done by gas) x2 F x1 Rewrite as w A Adx x1 F Opposing pressure is Pex A Pressure of gas= P; and volume change is dV Adx V2 Therefore, work : w Pex dV V1 px P Pex gas will expand; gas will be compressed P Pex P Pex equilibrium. No change in volume of gas. CHAPTER 2: FIGURE 2A.6 V2 w Pex dV V1 PHYSICAL CHEMISTRY: QUANTA, MATTER, AND CHANGE 2E| PETER ATKINS| JULIO DE PAULA | RONALD FRIEDMAN ©2014 W. H. FREEMAN D COMPANY Gas Expansions • Gas expansions are technologically important for steam engine, internal combustion engine, refrigerator, air conditioner • Isothermal Expansion the gas is in thermal contact with its surroundings; temperature is constant; T = 0 • Adiabatic Expansion No heat enters gas during expansion; q = 0 V2 • Work done by gas expanding w Pex dV V1 Larger the opposing pressure, the more work done. (But Pex < P, or 0 work done) • How to maximize work? Consider ideal gas with P1 = 10 atm and V1 = 1 L. Pex = 10 atm (1 atm from air and 9 atm from weights) If remove all weights at once, If move weights in 2 steps w 521 5L atm gas will expand until P1=Pex; step 1: Pex = 5, gas expands to 2 L final volume of 10 step 2: Pex = 1, gas expands to 10 L w 110 2 8L atm More work! w 1atm10 1L 9L atm 912J w 13L atm 1318J Reversible Process • Can maximize work if P = Pex + dP at each stage of expansion nRT • In the limit of dP 0 with Pex P V for reversible expansion or compression of ideal gas V2 V2 nRT w p dV dV nRT ln(V /V ) ex V 2 1 V1 V1 • This limiting case is an example of a reversible process. Reversible change: a change that occurs through a series of equilibrium states; has to occur slowly enough to establish an equilibrium. • Occurs in the limit of an infinite number of infinitesimal steps. • Tells us the maximum work that can be obtained from a process. • Important because it simplifies thermodynamic calculations -- Can use P in place of Pex -- State Variables depend only on final and initial state and not on path. Can calculate changes along reversible path; will be the same for an irreversible path between the same points. Irreversible expansion: external pressure and the pressure of the gas are not in in equilibrium during the expansion e.g. expansion into a vacuum Other Work U = q + wexp + we PHYSICAL CHEMISTRY: QUANTA, MATTER, AND CHANGE 2E| PETER ATKINS| JULIO DE PAULA | RONALD FRIEDMAN ©2014 W. H. FREEMAN D COMPANY Temperature vs. Heat Temperature (T, K) Heat (q, J) Intensive Extensive Based on ideal gas in limit of low P All forms of energy transfer not due to work. (true for real gases) Ind. of material used Associated w/ a thermodynamic process. Scale chosen so entropy at 0 K is 0 ; The transfer of energy by heat to a pure 푇 = 푘 lim 푃푉 substance will change its T, depending on its 푃→0 heat capacity. Heat Capacity Heat Capacity Proportionality between the q and the T- change it produces CT dq C not constant, depends on T dT Depends on whether material is allowed to expand Extensive property dq Heat capacity at constant Cv dT volume v 1 dq Cvm Molar Heat Capacity n dT v Specific Heat 1 dq cv (w = mass) w dT v Internal Energy and Heat Capacity at Constant Volume U U Consider U(T,V); Use slope formula dU dT dV T V V T Change state infinitesimally: dU=dq+dw U (1) only PV work: dU=dq-PexdV dU dT dq (2) If constant volume dV = 0 T V dq U CVm C dTV Vm T V U What about second slope? V T Called Internal Pressure, π. (will derive later) U P T P V T TV nRT Find internal Pressure of Ideal Gas P V Internal energy of an ideal gas depends only on temperature! Equation of State for U Putting the slopes together, we get P dU CvdT T P dV TV 1. Ideal gases: second term is 0. 2. Real gases at low to moderate P: second term is small. "near ideal" 3. Constant Volume (dV=0): Second term is 0. 4. Condensed Phases: Internal Pressure is large, but dV is small. Often neglect second term. So, in many cases, consider U(T): T2 U CvdT T1 Shows that internal energy is useful for constant volume processes CHAPTER 2: FIGURE 2E.1 PHYSICAL CHEMISTRY: THERMODYNAMICS,QUANTA, MATTER, AND STRUCTURE, CHANGE 2E|AND PETER CHANGE ATKINS| 10E | JULIO PETER DE ATKINS PAULA | |JULIO RONALD DE PAULA FRIEDMAN ©2014©2014 W. H. FREEMAN ANDD COMPANY COMPANY Enthalpy (H) Definition of enthalpy H = U+PV Changes in enthalpy of the system is equivalent to the heat exchanged between the system and surroundings under constant pressure. dH = dU+d(PV) = dq – PdV + PdV + VdP Thus, dH = dq +VdP dH= dq (at constant P) Enthalpy is convenient to describe heat transfer in and out of the system during the physical and chemical changes under constant pressure conditions. e.g. under atmospheric pressure. Equation of State for H(T,P) H H Slope equation dH dT dP TP PT • Take this at constant P (dP = 0) H dH dT dqP TP H • First term is heat capacity at constant P CP TP H V • Second term is (will derive later) V T P T TP V • Overall equation of state dH CPdT V T dP T P 1. Ideal gases: second term is 0. For ideal gases, enthalpy depends only on T. 2. Constant pressure (dP=0): Second term is 0. First term tends to be more important T 2 H C dT Change in enthalpy when T is changed from T1 to T2 at constant P P T1 CPm depends on T for polyatomic gases, liquids and solids Comparison of internal energy and enthalpy V1 • U - used in constant V processes V1 P2 > P1 • H - used in constant P processes P1 • C - constant volume heat capacity, related U = q v constant V to U • C - constant pressure heat capacity, gas p Heat related to H (q) • If V = 0, w = 0, so U = q V2 > V1 • If P = 0, H = q P For an ideal gas, if gas 1 • T = 0, H = U = 0!!! U = q + w = q – p1V constant Pex gas H = U + (PV) Internal energy is lower = q – P1V + P1V than the heat transferred = q under constant P Why does C change w/T? -1 -1 -1 3 3 • Average translation energy is (per molecule; kb (JK ) or permole R (JK mole )) tr 2 kbT tr 2 RT • Energy increase upon addition of heat is reflected in an increase in temperature 3 q 2 RT2 T1 q/T=C 3 • Therefore, molar heat capacity is Cvm 2 R • Only correct for closed shell atoms at low densities.