Heat What is heat? Work = 2. PdV 1
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1 eat What is heat? eat (Q) is the flow or transfer of energy from one system to another Often referred to as heat flow or heat transfer Requires that one system must be at a higher temperature than the other eat will only flow from the system with the higher temperature to the system with the lower temperature eat will only flow from the system with the higher average internal energy to the system with the lower average internal energy Total internal energy does not matter. Work W = 1 Pd 1
2 First aw of Thermodynamics When temperature changes, internal energy has changed may happen through heat transfer or through mechanical work First law is a statement of conservation of energy Change in internal energy of system equals the difference between the heat added to the system and the work done by the system Differential form ΔU = Q W du = dq dw eat added +, heat lost -, work done by system +, work done on system Internal Energy U is a state property Work W and heat Q are not But work and heat are involved in thermodynamic processes that change the state of the system Molar Specific eats for Gasses Molar specific heats for gasses are different if heat is added at constant pressure vs. constant volume Q P = nc P ΔT Q = nc ΔT Isobaric, ΔP = 0 W = PΔ Q P = ΔU + PΔ Isochoric, Δ = 0 W = 0 Q = ΔU If the two processes result in the same temperature change, ΔU is the same. Q nc ΔT nc ΔT = nrδt C P = Q P C P PΔ = R
3 Types of Transformations Isothermal, ΔT = 0 ΔU = 0, W = Q Work done by the system equals the heat added to the system B B nrt W = Pd = d A A Adiabatic, Q = 0 ΔU = -W = nrt ln Work done by the system lowers the internal energy of the system by an equal amount Temperature can change only if work is done. γ 1 1 C W adiabatic = P constant, where γ 1 C P = γ = B A P P Types of Transformations Isobaric, ΔP = 0 W = PΔ Work = Pressure*Change in ol W B = Pd = P A B A d = P ( ) B A ΔU calculated from 1 st law Isochoric, Δ = 0 W = 0 ΔU = Q The change in internal energy of the system equals the heat added 3
4 eat Transfer Conduction Results from molecular interactions Collisions? Energy is transferred through interaction Convection Results from the mass transfer of material Think fluid flow Radiation Energy transferred by electromagnetic radiation (waves) Does not require a medium Δ T T = ka Δt l Q 1 l R-alue: R = k dq dt = ka dt dx ΔQ = eσat Δt 0 e 1 4 σ = W / m T1 T = A R K 4 Net heat flow between two objects 4 4 ( ) ΔQ = eσa T 1 T Δt Reversible & Irreversible Processes Example of a Reversible Process: Cylinder must be pulled or pushed slowly enough (quasistatically) that the system remains in thermal equilibrium (isothermal). Change where system is always in thermal equilibrium: reversible process Change where system is not always in thermal equilibrium: irreversible process Examples of irreversible processes: Free expansion of a gas Melting of ice in warmer liquid Frictional heating Anything that is real All real processes are irreversible! 4
5 eat Engine An engine is a device that cyclically transforms thermal energy (heat?) into mechanical energy (useful work). Efficiency: Fraction of heat flow becomes mechanical work: W Q Q e = = = 1 A minimal version of an engine has two reservoirs at different temperatures T and T, and follows a idealized reversible cycle known as the Carnot cycle. Efficiency of the Carnot cycle Realistically, What is T? What is a reasonable e C? e W Q C = = 1 = 1 T T eat Pumps, Refrigerators, and Air Conditioners eat pumps, refrigerators, and air conditions are engines run in reverse: Refrigerator and air conditions remove heat from the cold reservoir and put it into the surroundings (hot reservoir), keeping the food/room cold. A heat pump takes energy from the cold reservoir and puts it into a room or house (hot reservoir), thereby warming it. In either case, energy must be added! Work must be performed ON the system! 5
6 eat Pumps and Refrigerators Since the (idealized) Carnot engine is the most efficient heat engine, the Carnot refrigerator is the most efficient refrigerator. Coefficient of Performance: Q Q T CP = = = W Q Q T T eat Pumps work similarly but have a different objective, namely warm the house. Coefficient of Performance: Q CP = W = Q Q T = T T The Second aw of Thermodynamics There are many ways of expressing the second law of thermodynamics; here are two: The Clausius form: It is impossible to construct a cyclic engine whose only effect is to transfer thermal energy from a colder body to a hotter body. Spontaneous heat flow always goes from the highertemperature body to the lower-temperature one. The Kelvin form: It is impossible to construct a cyclic engine that converts thermal energy from a body into an equivalent amount of mechanical work without a further change in its surroundings. Thermal energy cannot be entirely converted to work. A 100% efficient engine is impossible. These definitions are incomplete! 6
7 Entropy and the Second aw Entropy is a measure of disorder. There is some controversy about this! The process of creating disorder (as well as order) increases entropy. Entropy is a measure of the energy unavailable to do work. It is a measure of the dispersal of energy. Energy is dispersed (used up?) in processes that create both order and disorder. Entropy and the Second aw The entropy of an isolated system never decreases; spontaneous (irreversible) processes always increase entropy. All the consequences of the second law of thermodynamics follow from the treatment of entropy as a measure of disorder. (?) Making engines that would convert mechanical energy entirely to work would require entropy to decrease in isolated system can t happen. Many familiar processes increase entropy shuffling cards, breaking eggs, and so on. We never see these processes spontaneously happening in reverse a movie played backwards looks silly. This directionality is referred to as the arrow of time. So, to what state is the universe heading? 7
8 A P- diagram for a reversible heat engine in which 1.00 mole of argon, a nearly ideal monatomic gas, is initially at STP (point a). Points b and c are on an isothermal. If the engine produces positive work, a) is the cycle clockwise or counter clockwise, b) what is the efficiency of the cycle? 8
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