Thermodynamics

1
Thermodynamics

• Walker, Chapter 18
• Physics 111
• Autumn 2003
• Prof. C.E. Hyde-Wright

2
Thermodynamics

• The 19th century industrial revolution was
  powered by the practical applications of the new
  understanding of the theoretical connection
  between heat and mechanics.
• Thermodynamics is the study of the connection
  between mechanics and average internal properties
  of a large system.
• In spite of its approximate character,
  Thermodynamics has emerged essentially intact,
  even strengthened by the twin 20th century
  revolutions of Relativity Quantum Mechanics
• Thermodynamics has also made important
  contributions to Cosmology.

3
Heat and Energy

• Dissipative mechanical processes produce heat.
• DE lt 0
• As a gas is heated, the pressure increases,
• If the gas is allowed to expand in a piston, the
  gas does mechanical work on its surroundings
• DE gt 0

4
Zeroth law of Thermodynamics(but last to be
enumerated)

• If object A is in thermal equilibrium with object
  C,
• And object B is in thermal equilibrium with
  object C,
• Then object A B are also in thermal
  equilibrium.
• Thermal Equilibrium Same temperature
• Thermal Equilibrium No heat flow
• BUT we often speak of a system in equilibrium
  heat flow between a system and a heat bath, which
  will happen if the two are at infinitessimally
  different temperatures.

C
A
T
T?dT
5
A Zen Koan for Zeroth Law of Thermodynamics(If
it is so obvious, how come no one thought of it
until after Laws 1, 2, 3)

• If system A and system B are in thermal
  equilibrium with each other, then by definition
  no heat flows from A to B (or vice-versa).
• In many thought-experiments (and real
  experiments) of thermodynamics, a system A is in
  thermal equilibrium with a much larger system B.
• B is called a heat bath
• The purpose of B is for B to keep a constant
  temperature, while exchanging any amount of heat
  ( or -) from A.
• But how can A B exchange heat if they are in
  thermal equilibrium (which was the whole point, B
  regulates the temperature of A)???

6
First Law of ThermodynamicsConservation of Energy

• In addition to mechanical energy (Kinetic Energy
  K, potential energy V) a system has internal
  thermal energy we label U.
• In any interaction of the system with its
  surroundings in which the system does mechanical
  work W and heat Q flows into the system, energy
  conservation requires that the change in internal
  energy of the system equals the heat flow in
  minus the work done (note signs).
• DU Uf -Ui Q - W
• Ultimately, Internal energy is not a new form
  of energyit is just the kinetic and
  chemicalelectromagnetic potential energy of
  the atoms and molecules that make up the matter
  of our system.

7
U, W, Q

• W work done by a system on its surroundings
• Q Heat flow into system (Qlt0 for heat flowing
  out).
• W and Q depend upon the particular process (e.g.,
  path in a Pressure vs Volume plot).
• U internal (thermal) energy of system.
• U depends only on the present state of the system
  (not on how it got there).
• For an ideal gas, U is a function only of
  Temperature.
• Monoatomic ideal gas (He, Ne, Ar) U (3/2) RT
• Diatomic ideal gas (O2, N2,) U (5/2) RT
• Need Quantum Mechanics to prove this!

8
Internal Energy of an ideal gas.

• Ideal gas U is a function only of temperature,
  not of P, V separately.
• U(ideal gas) kinetic energy of molecules
  internal rotational and vibrational energy. This
  is independent of the volume.
• Place an ideal gas in a container of volume V.
  Suddenly double the volume (open a valve to a 2nd
  container), kinetic energy of gas does not
  change, the gas does no work.
• Temperature does not change, U is unchanged.

Kinetic Theory simulations http//physics.weber.e
du/schroeder/software/
9
First Law of ThermodynamicsSpecial case I.
Constant Volume

• The system does no work (a gas at fixed volume)
• Change in internal energy Heat flow in
• DU Q n CV DT

CV molar specific heat at constant volume
10
First Law of ThermodynamicsII. Thermally isolated

• No heat flows in or out of the system
• A gas expands in a piston, but the system is
  thermally isolated, the expansion happens too
  fast for any significant exchange of heat.
• DU -W
• Thermal energy is converted to work.
• If Uf lt Ui then the system does positive work on
  its surroundings.

11
Thermal ProcessesExpansion at Constant Pressure

• A gas expands, pushing a piston at constant
  pressure.
• The gas exerts a force F P A against the piston
• The gas does work W F(xf-xi)
• W P A (xf-xi)
• W P (A xf- A xi )
• W P (Vf Vi)
• W P DV

Work Area under a pressure vs. Volume curve
12
Constant Pressure ExpansionExample

• Approximate the power stroke of a 4-cylinder
  automobile engine by a constant pressure
  expansion at P 10 atm with a change in volume
  of DV0.5 litre. If the engine is running at
  3000 rpm, what is the total power output of the
  engine in Watts, and Horsepower.
• Find the engine torque.

1 litre (10 cm)3 (0.1 m)3 1.010-3 m3 T
time for one complete engine cycle Four stroke
engine, T two engine revolutions T 2/f 2 /
3000 revolutions / min T (1 min) / 1500 (60
sec/min)(1 min/1500) 1sec/25 0.04 s
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Engine Power, contd

• Work done by one cylinder
• W PDV 10(105 N/m2) (0.5 10-3 m3) 5 102 N
  m
• Total power rate at which all four cylinders do
  work
• Power 4 W / T
• Power 4 (5 102 J) / (0.04 sec) 50 kWatt
• Power (50 kWatt) (1 hp)/(746 W) 67 hp
• Power force times velocity Torque times
  angular velocity (chap 10, not on exams)
• Torque power divided by angular velocity
• Angular velocity 2p f (2p) 3000/min 2p
  50/sec 314/sec
• Torque (50kW) / (314/s) 16 N m
• Convert N m to ftlb.
• 2.2lb (1kg)(g) 9.8 N
• 1ft ? 30 cm
• Torque 16 N m 2.2lb/9.8N 1ft/0.3m 12
  ftlb.

14
Ideal Gas Molar Heat Capacity at Constant Pressure

• An ideal gas expands against a constant pressure
  from C to B
• DU QCB WCB
• UB-UC nCP(TB-TC) PC (VB-VC) nCP(TB-TC) n
  R(TB-TC)
• CP molar heat capacity at constant pressure

• If instead the gas is heated from C to A,
• UA-UC nCV(TA-TC)
• Also, UB UA (isotherm)
• UA-UC UB-UC
• CP CV R

15
Thermal ProcessesIdealized Reversible Processes

• An ideal gas is confined by a piston, which
  exerts a variable pressure P. The gas is
  isolated, no heat enters or leaves the gas.
• The external pressure P slowly compresses the gas
• Ideal Gas Law, PV n R T
• As the piston compresses the gas, the gas does
  work on the piston W PDV lt 0
• The internal energy of the gas rises DU Q -W
  -W gt0
• If the internal energy rises, the temperature
  rises.
• We will find out how to calculate the temperature
  rise later.

16
Reversible Process with Heat Bath(Isotherm)

• An ideal gas is confined by a piston, which
  exerts a variable pressure P.
• The gas is in contact with a heat bath at
  temperature T.
• The external pressure P slowly compresses the
  gas, this tends to head the system to
  temperature TdT, but heat flows out of the
  system to the heat bath, keeping its constant
  temperature T.
• Now reverse the process, the gas expands against
  the pressure P, Heat flows into the system to
  keep the temperature constant
• 0 DU Uf -Ui Q - W

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Isotherms
PVnRT PnRT/V
18
Work done by system in isothermal process (T
constant)

• 0 DU Q-W Q W
• Volume changes from Vi to Vf
• Break up process into small steps
• Volume changes by dV ltlt DV with each step.

19
Logarithms

• Log(u) v means 10v u
• ln(x) y means eyx e2.71828
• if eyx, ln(x) lney y by definition of
  ln().
• Logarithms are just a way of making big numbers
  small
• log(10 trillion) 13
• and turning multiplication into addition

20
Otto Cycle

• 4-stroke
• 1) Compress fuel/air mixture
• Explosive burn (nearly instantaneous).
• 2) Adiabatic expansion
• 3) Exhaust
• 4) Fuel/Air intake

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Adiabatic Process(thermally isolated system, no
heat in or out)

• Need Calculus to show
• PVg constant
• g Cp / CV
• Calculus also needed to calculate work done.
• DU Q-W
• DU -W

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2nd Law of Thermodynamics

• First Version
• When objects of different temperature are brought
  into thermal contact, the spontaneous flow of
  heat is always from the hotter object to the
  cooler object

23
Heat Engine

• A heat engine is a mechanical system that as it
  cycles through a repetitive motion, transfers
  heat from a high temperature heat bath to a low
  temperature bath, and performs work on its
  environment
• Qh W Qc
• Examples
• Diesel cycle auto.howstuffworks.com/diesel.htm
• Otto cycle (gasoline engine)
• Stirling Engine
• Carnot cycle (idealized heat engine).

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Carnot Cycle

• Isothermal expansion
• Heat in from high temperature bath
• W1 gt 0
• Adiabatic expansion
• No heat in or out
• W2 gt 0
• Isothermal Compression
• Heat dumped into low temperature bath
• W3 lt 0
• Adiabatic Compression
• No heat in or out
• W4 lt 0
• Net work shaded area net area under P vs V
  graph.

The heat engine alternates between contact with
high and low temperature reservoirs
25
Carnot Cycle Efficiency

• In the ideal Carnot cycle, a heat engine operates
  in a closed loop, absorbing heat QH at high
  temperature TH, and discharging heat QC at cool
  temperature TC, while doing work W. The
  efficiency is defined by
• Efficiency e W/QH a
• For the ideal carnot cycle, e 1 TC/TH
• (temperature measured from absolute zero).
• 2nd Law of Thermodynamics (heat engine version)
• A heat engine has maximum efficiency if all
  proceses are reversible
• All heat engines operating between TC TH have
  the same efficiency
• No heat engine, operating between temperatures TH
  and TC can have a higher efficiency than the
  Carnot cycle.

26
Walker, problem 86

• A mole of an ideal monoatomic gas follows the
  three part cycle shown. Fill in the table, and
  find the efficiency of this cycle.

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Walker, problem 86, solution

• B?C, constant pressure compression
• W P DV, note DV(VC-VB) lt 0
• Q n CP DT
• Use PV nRT to find TB, TC
• DU Q-W nCP DT - P DV nCP DT n R DT nCV
  DT
• Ideal Gas U nCV T DU nCV DT

• C?A, Constant volume heating
• W 0 (no change in volume)
• Q nCV DT
• DU Q W nCV DT
• A?B, Isotherm, DU 0
• W n R lnVB/VA
• 0 DU Q W
• Q W

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Steam Engine Not an ideal gas!!

• In the piston, the hot water vapor expands along
  an adiabad no heat in or out.
• In the condensor, the water vapor (T100C)
  condenses to liquid (T100C) while liberating
  heat Latent heat to the heat bath (Tlt100C)
• The pump maintains the pressure difference
  between condensor and boiler. Since liquid is
  almost incompressible, pump does almost no work.
• In the boiler, the water at 100C absorbs latent
  heat from heat bath (Tgt100C) and boils.

boiling
Adiabad
condensing
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Quiz 11, Nov 24, 2003
Name Signature

• Ideal Gas Law, PV nRT
• Calculate the ratio Pf /Pi in each case.
• Double the volume at constant Temperature.
• Double the volume and double the temperature.
• Keep volume and Temperature constant, double the
  number of molecules in the container.

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Dec 1

• Heat Engines
• 2nd Law of Thermodynamics
• Entropy
• Put some chocolate chips into soda pop, and I
  will explain how that is a demonstration of the
  2nd law of thermodynamics.
• 3rd Law of Thermodynamics
• Semester Review / Final exam Preview.

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Heat Pump

• A heat engine, run in reverse, is a heat pump.
• It pumps heat from the cool temperature to the
  hot temperature.
• This violates the 2nd law of thermodynamicsNOT,
  because the net work done by the system is
  negative (There must be work done on the system).
• Examples
• Refridgerator
• What happens to temperature in room if you leave
  the refridgerator door open?
• Air Conditioner
• Heat pump for heating house.
• Coefficient of performance QH/W

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Entropy Measure of Disorder

• Entropy is a state variable (like thermal energy)
• Changes in entropy S
• DS Q/T
• Chocolate chip motor Entropy engine (see my web
  page).

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Third Law of Thermodynamics

• It is impossible to reach absolute zero in a
  finite number of steps.