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Work in Thermodynamic Processes. Energy can be transferred to a system by heat and/or work The system will be a volume of gas always in equilibrium Consider a cylinder with a movable piston As piston is pressed a distance Δ y, work is done on the system reducing the volume

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work in thermodynamic processes
Work in Thermodynamic Processes
  • Energy can be transferred to a system by heat and/or work
  • The system will be a volume of gas always in equilibrium
  • Consider a cylinder with a movable piston
    • As piston is pressed a distance Δy, work is done on the system reducing the volume

 W = -F Δy = - P A Δy

work in thermodynamic processes cont
Work in Thermodynamic Processes – Cont.
  • Work done compressing a system is defined to be positive
    • Since ΔV is negative (smaller final volume) & A Δy = V

 W = - P ΔV

    • Gas compressed  Won gas = pos.
    • Gas expands  Won gas = neg.
work in thermodynamic processes cont1
Work in Thermodynamic Processes – Cont.
  • Can only be used if gas is under constant pressure
    • An isobaric process (iso = the same) P1 = P2
    • Represented on a pressure vs. volume graph – a PV diagram
    • Area under any curve = work done on the gas
    • If volume decreases – work is positive (work is done on the system)

First Law of Thermodynamics

  • Energy is conserved
  • Heat added to a system goes into internal energy, work or both
    • ΔU = Q + W
    • Heat added to system  internal energy  Q is positive
    • Work done to the system  internal energy  W is positive (again)
first law cont
First Law – Cont.
  • A system will have a certain amount of internal energy (U)
  • It will not have certain amounts of heat or work
    • These change the system
  • U depends only on state of system, not what brought it there
    • ΔU is independent of process path (like Ug)
isothermal process
Isothermal Process
  • Temperature remains constant
  • Since P = N kB T / V= constant / V
    • An isotherm (line on graph) is a hyperbola
isothermal process cont
Isothermal Process – Cont.
  • Moving from 1 to 2, temperature is constant, so P & V change
  • Work is done = area under curve
  • Internal energy is constant because temperature is constant

 Q = -W

  • Heat is converted into mechanical work
isometric isovolumetric process
Isometric (isovolumetric) Process
  • The volume is not allowed to change
    • V1 = V2
  • Since no change in volume, no work is done

 ΔU = Q

  • Heat added must go into internal energy  it
  • Heat extracted is at the expense of internal energy  it
isometric process cont
Isometric Process – Cont.
  • The PV diagram representation
    • No change in volume
    • Area under curve = 0
    • That is, no work done
    • The process moves from one isotherm to another
isobaric process
Isobaric Process
  • As heat is added to system, pressure is required to be constant
    • The ratio of V / T = constant
    • Some of the heat does work and the rest causes a change in temperature
    • Thus moving to another isotherm
    • Recall: changes in temperature = changes in internal energy

 ΔU = Q + W

adiabatic process
Adiabatic Process
  • No heat is transferred into or out of system
  • Q = 0

 ΔU = W

  • All work done to a system goes into internal energy increasing temperature
  • All work done by the system comes from internal energy & system gets cooler
adiabatic process cont
Adiabatic Process – Cont.
  • Either system is insulated to not allow heat exchange or the process happens so fast there is no time to exchange heat
adiabatic process cont1
Adiabatic Process – Cont.
  • Since temperature changes, we move isotherms
the second law of thermodynamics heat engines
The Second Law of Thermodynamics & Heat Engines
  • Heat will not flow spontaneously from a colder body to a warmer
  • OR: Heat energy cannot be transferred completely into mechanical work
  • OR: It is impossible to construct an operational perpetual motion machine
heat engines
Heat Engines
  • Any device that converts heat energy into work
    • Takes heat from a high temperature source (reservoir), converts some into work, then transfers the rest to surroundings (cold reservoir) as waste heat
heat engines cont
Heat Engines – Cont.
  • Consider a cylinder and piston
    • Surround by water bath & allow to expand along an isothermal
    • The heat flowing in (Q) along AC equals the work done by the gas as it expands (W) since ΔU = 0
    • To return to A along same isothermal, work is done on the gas and heat flows out
    • Work expanding = work compressing
heat engines cont1
Heat Engines – Cont.
  • A cycle naturally can have positive work done
  • In going from A to B work is done by gas, temperature  (ΔU ) and heat enters system
  • B to C
    • No work done, T , ΔU , & heat leaves system
  • C to A
    • ΔU = 0, heat leaving = work done
    • The work out = the net heat in (ΔU = 0)
heat engines cont2
Heat Engines – Cont.
  • Thermal Efficiency
    • Used to rate heat engines
    • efficiency = work out / heat in

 e = Wout / Qin

    • Qin = heat into heat engine
    • Qout = heat leaving heat engine
  • For one cycle, energy is conserved

 Qin = W + Qout

  • Since system returns to its original state ΔU = 0
the carnot engine
The Carnot Engine
  • Any cyclic heat engine will always lose some heat energy
    • What is the maximum efficiency?
    • Solved by Sadi Carnot (France) (Died at 36)
    • Must be reversible adiabatic process
the carnot engine cont
The Carnot Engine – Cont.
  • Carnot Cycle
    • A four stage reversible process
    • 2 isotherms & 2 adiabats
    • Consider a hypothetical device – a cylinder & piston
    • Can alternately be brought into contact with high or low temperature reservior
    • High temp – heat source
    • Low temp – heat sink – heat is exhausted
the carnot engine cont1
The Carnot Engine – Cont.
  • Step 1: an isothermal expansion, from A to B
    • Cylinder receives heat from source
  • Step 2: an adiabatic expansion, from B to C
the carnot engine cont2
The Carnot Engine – Cont.
  • Step 3: an isothermal compression, C to D
    • Ejection of heat to sink at low temp
  • Step 4: an adiabatic compression, D to A
  • Represents the most efficient (ideal) device
    • Sets the upper limit
  • A measure of disorder
    • A messy room > neat room
    • Pile of bricks > building made from them
    • A puddle of water > ice came from
  • All real processes increase disorder  increase entropy
  •  of entropy of one system can be reduced at the expense of another
entropy cont
Entropy – Cont.
  • Entropy of the universe always increases
  • The universe only moves in one direction – towards  entropy
  • This creates a “direction of time flow”
    • Nature does not move systems towards more order
entropy cont1
Entropy – Cont.
  • As entropy , energy is less able to do work
    • The “quality” of energy has been reduced
    • Energy has “degraded”
  • Nature proceeds towards what is most likely to happen