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   U = 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   U = Q + W  Work done on system is positive  Heat leaving system is negative  Implication: When  U = 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 1. Isothermal (no temperature change)  T =  U = 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  T =  U = 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? If Q = 0 is  U positive or negative? What about the temperature? Compression, since V decreases  U and  T 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  U = 0 + (W) T increases In diesel fuel-air mixture ignites spontaneously

Work If pressure constant W = -Fd = -PAd = -P  V Work negative if expansion Work positive if compression Remember new convention: work done ON is positive

Calculating Work P  V Work done by a gas equals area under PV curve FIND THE WORK! Hint: 1 atm = 10 5 N/m 2 ; 1l = m 3 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 V 2atm J J 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  U = U f – U i = 3/2nR(T f – T i ) 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 Q 1 at a high temperature is partly transformed into work W. The waste heat Q 2 is exhausted at a lower temperature

QHQH W QLQL Q H = W + Q L Efficiency = W/Q H

Carnot Engine: most efficient (ideal)

Efficiency = useful work/ Q H = W/ Q H = (Q H -Q L )/Q H Q H = W + Q L ;Q H is at operating temperature Eff = 1 – Q L /Q H ; Q L is exhaust heat Eff ideal = 1 – T L /T H 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/Q H = 2/5 An ideal engine operates between 900 and 500 degrees. Find efficiency Eff = 1 – T L /T H = 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 Q: Will your kitchen be hotter or colder with the refrigerator door open? CP = Q 2 /W = Q 2 /(Q 1 -Q 2 ) Coefficient of performance W is work done by motor/com pressor

Entropy Change in entropy S of a system when heat Q is added to it is  S = 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