Work in Thermodynamic Processes

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Work in Thermodynamic Processes - PowerPoint PPT Presentation

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
• 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 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 – 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)
THERMODYNAMICS

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.
• 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
• Temperature remains constant
• Since P = N kB T / V= constant / V
• An isotherm (line on graph) is a hyperbola
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
• 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.
• 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
• 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

• 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
• Either system is insulated to not allow heat exchange or the process happens so fast there is no time to exchange heat
• Since temperature changes, we move isotherms
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
• 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.
• 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 – 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 – 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
• 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.
• 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 – 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 – 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
Entropy
• 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 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 – Cont.
• As entropy , energy is less able to do work
• The “quality” of energy has been reduced