September 28, 2013

Diego VillarrealSHP – Columbia University

Thermodynamics & Energy Conversions

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What is energy anyway?

• Energy? “Capacity to do work”• Different types of energy:

○ Mechanical• Kinetic – Associated with object or fluid motion (KE = ½ mv2)• Potential – Associated with object’s position (PE=mgh)

○ Chemical energy – Energy stored in chemical bonds and released upon transformation/reaction (coal, oil, methanol)

○ Nuclear – Energy found within the atomic nucleus. Can be released by ‘breaking’ (fission) the atoms.

○ Thermal Energy – Think of it as microscopic PE & KE of an object that results in its temperature (cup of hot coffee).

○ Radiant – Energy of electromagnetic waves.○ Electrical –

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Wasted energy• About 3/5 of the fuel energy input is

“wasted”. • Because our energy system is highly

dependent on fossil fuels this leads to extra CO2 and pollution.

• So, why is this? Is there a natural limit to how efficient we can be at our energy conversion?

• Need to turn to thermodynamics to answer this question.

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Energy, Heat and work

• Main principles:○ Heat spontaneously flows from Hot

Cold (Always, no exception). More formal treatment of this in a bit.

○ Energy Conservation - Energy can be transformed from one form to another, but cannot be created or destroyed.

• Thermodynamics – The study of the interchangeability of heat and work. ○ Think of thermodynamics as the “economics of science”.

It will tell us how much we will have to “pay” for particular transformations and whether or not they are feasible.

○ Basic “bookkeeping”

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Heat

• Heat (Q) is the energy transferred between a system and its surroundings (other than by work). Usually a result of a temperature difference between two objects.

• Heat is NOT a fluid and is never contained within an object; an object contains thermal energy.

• Think of ΔT as an “index” of your ability to move heat. Remember this!

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First law of thermo

• First law of thermo?○ The first law of thermodynamics states that during any cycle that a

system undergoes, the cyclic integral of the heat is equal to the cyclic integral of the work. Hence, it requires that energy be conserved during a process. However, the first law places no restrictions on direction of flow.

• That is, work done on a system plus the heat added to it is equal to the total change in energy of the system. ΔE = Won +

Qto

• Work done on a system is the negative of work done by the fluid (Won=-Wby) so:

Qto= ΔE + Wby

• Temperature does not tell us the amount of energy contained in a substance. However a change in temperature tells us something about the heat added (removed)

Q = mcΔT

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Second law

• Second law?○ The only processes that can occur are ones that

result in an increase in the entropy of the systems (e.g. direction matters!)

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Heat Engines

• We know from experience that work can easily be converted to other forms of energy, but converting other forms of energy to work in not that easy.

• Converting heat to work requires the use of some special devices. These devices are called heat engines.

1. HE receive heat from a high-temp source

2. Convert part of this heat to work (usually by rotating shaft)

3. Reject the remaining waste heat to a low temperature reservoir.

4. Operate in a cycle

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PV diagrams

• Useful tool to study heat engines.

• Points ab are at constant T. Called “isotherms”.• So moving from a represents “Isothermal

Expansion”

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Adiabatic compression

• Looking at the PV diagram, what is a necessary condition to perform isothermal compression/expansion?○Heat must be supplied or removed!

• So what happens if I insulate the compression chamber or do fast compression?○ΔQ = 0!○ Thermal energy and T must change.○ “Adiabatic” compression/expansion

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Carnot Engine

• Let’s do a device to exchange Q and W using isotherms and adiabats.

• Assumptions:○ Piston-Cylinder device○ Perfectly insulated but insulation is such

that it can be removed instantaneously to put system in contact with heat reservoir.

○No friction, no turbulence○No mechanical inefficiency losses

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Carnot Cycle

• Step 1-2: Isothermal Expansion• Step 2-3: Adiabatic Expansion• Step 3-4: Isothermal Compression• Step 4-1: Adiabatic Compression

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Carnot Efficiency

• Wnet will be area enclosed by engine cycle. • Important question: what fraction of the heat

supplied is converted to mechanical work?○ Called the efficiency!○ Efficiency = Wout/Qin

○ η = (Qin-Qout)/Qin

• For carnot engines:

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Steam cycle• The core of a steam power

consists of four components: ○ a boiler, turbine,

condenser, and a pump. • First, fuel is burned in a

furnace/boiler where the released heat is transferred to pressurized water contained within steel tubes.

• Then, the high-pressure, high-temperature steam is delivered to a turbine.

• Steam generated in this process is expanded in a steam turbine, which drives an electric generator to produce electric power.

• Steam is later cooled down in a condenser and is pumped back to the boiler to be reheated, completing the cycle.

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Carnot example

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Other Carnot Examples