Thermodynamics How Energy Is Transferred As Heat and Work Animation Courtesy of Louis Moore
How Internal Energy can Increase • Heat can be added (Symbol Q) • Mechanical Work can be done on the system(like a piston compressing gas) (Symbol W)
The First Law - • DU = Q + W • U is internal energy • +Q is heat added (absorbed) • +W is net work done on system • The first law is a restatement of the law of conservation of energy
Piston and Cylinder
Sign Conventions • DU = Q + W • Work done on system is positive • Heat leaving system is negative • Implication: When DU = 0, Q = -W Reminder: U = 3/2nRT = 3/2 NkT
Examples • (1) 1000 J of heat is added to the system and 500 j of work is done on the system. What is the change of internal energy? • (2) 300 J of heat escapes and 200 J of work is done by the system. What is the change of internal energy? Answer: 1500 J Answer: -500 J
Processes • Isothermal (no temperature change) DT = DU = 0 ; PV = constant 2. Adiabatic (no heat flow in or out) Q = 0 3. Isobaric (no change in pressure) 4. Isochoric (no change in volume)
PV Diagram for Isothermal Process DT = DU = 0
Adiabatic Processes • No heat added or taken away • Examples: • Quickly pushing down a bicycle pump • Compression stroke in heat engine • Expansion in power stroke • Why adiabatic – too fast for any appreciable heat to enter or leave • Also if well insulated
PV Diagram for Adiabatic Process Q = 0 Happens when system is well insulated or if process happens very quickly as in rapid expansion of gases in an internal combustion engine.
Expansions or Compressions? Compression, since V decreases If Q = 0 is DU positive or negative? What about the temperature? DU and DT positive
PV Diagram for Isochoric Process
What does the PV Diagram look like for an Isobaric process? P V
What happens in compression stroke of an engine? • Adiabatic since fast • Work is done ON gas • U increases since DU = 0 + (W) • T increases • In diesel fuel-air mixture ignites spontaneously
Work Remember new convention: work done ON is positive • If pressure constant W = -Fd = -PAd = -PDV • Work negative if expansion • Work positive if compression
Calculating Work P DV • Work done by a gas equals area under PV curve FIND THE WORK! Hint: 1 atm = 105 N/m2 ; 1l = 10-3 m3 Answer: About 250 Joules
Work Along a Curved Path • Use calculus or graph paper to estimate
Work Around a Closed Path • Equals area enclosed on PV diagram • Negative for clockwise path • Positive for counter-clockwise path
First Law Example • An ideal gas is slowly compressed at constant pressure of 2.0 atm from 10L to 2L. With volume constant heat is added; pressure and temperature rise until temperature reaches its initial value. • Find total work done on gas • Find total heat flow into gas • Find net change in U? P +1600 J 2atm -1600 J V zero, since returns to initial value
How a Car Engine Works LINK TO “HOW STUFF WORKS”
Work Done in an Engine • 0.25 moles of gas expands quickly and adiabatically against piston. T drops from 1150 k to 400K How much work is done? • Hint: use DU = Uf – Ui = 3/2nR(Tf – Ti) Answer: 2300 J
Second Law of Thermodynamics • Heat flows naturally from hot to cold objects • No device can simply transform heat to work(100% efficient engine impossible) • A perfect refrigerator is impossible • The total entropy(disorder) of a system and its environment increases in natural processes
Heat Engines • Heat input Q1 at a high temperature is partly transformed into work W. The waste heat Q2 is exhausted at a lower temperature
QH = W + QL Efficiency = W/QH QH W QL
(ideal) Carnot Engine: most efficient
Efficiency • = useful work/ QH = W/ QH = (QH-QL)/QH • QH = W + QL ;QH is at operating temperature • Eff = 1 – QL/QH ; QL is exhaust heat • Eff ideal = 1 – TL/TH for Carnot Engine • Kelvin temperatures only
Examples • In one cycle of an engine 5000 j are released by burning and 3000 j are exhausted. What is efficiency? • Eff = W/QH = 2/5 • An ideal engine operates between 900 and 500 degrees. Find efficiency • Eff = 1 – TL/TH = 4/9
Heat Engine Facts • Gasoline engines operate at 15-25% efficiency • Diesel engines operate at 30-50%. They operate at higher temperatures • Many other engine designs exist such as Sterling engine
Refrigerator • Heat engine operated in reverse CP = Q2/W = Q2/(Q1-Q2) Coefficient of performance W is work done by motor/compressor Q: Will your kitchen be hotter or colder with the refrigerator door open?
Entropy • Change in entropy S of a system when heat Q is added to it is DS = Q/T According to Second Law of Thermodynamics, the entropy of an isolated system never decreases.
Entropy Examples • Molecules do not migrate to one corner of room • Dropped cup breaks; pieces do not spontaneously reassemble themselves • Hammer hitting nail heats it. Hammer on top of nail does not spontaneously rise up as nail cools • Mixtures do not separate by themselves
Heat Death • In any natural process some energy becomes unavailable to do useful work • Energy is degraded • Goes from most orderly form (mechanical) to least orderly (heat) • Eventually all energy of universe is degraded to heat; all change ceases
