The First Law of Thermodynamics

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Chapter 17

• The First Law of Thermodynamics

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Thermodynamic Concepts

• Thermodynamic systemable to exchange heat with
  its surroundings
• State variables p, V, T, ...describe the
  thermodynamic system
• Thermodynamic processchanges the state ( p, V,
  T, ...) of the system

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Thermodynamic Process

• Heat Q
• can leave or enter system
• Work W
• system can do work on its surroundings
• surroundings can do work on the system

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• thermodynamicsystem can exchange heat with its
  surroundings
• state of system(p, V, T, ...)
• thermodynamicprocesschanges state of the system

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• thermodynamicprocesschanges state of the system
• Well focus on the roles of
• Heat Q
• Work W

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• Heat Q can leave or enter system
• Q gt 0 heat added to system
• Q lt 0 heat removed from system

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Sign Conventions for Q

• Q gt 0 heat added to system
• Q lt 0 heat removed from system
• Consistent with sign of DT from earlier
• Q mc DT or Q nC DT

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• Work W
• W gt 0 system does work on its surroundings
• W lt 0 surroundings does work on the system

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Sign Conventions for W

• W gt 0 system does work on surroundings
• W lt 0 surroundings does work on system
• (the opposite perspective as in mechanics)

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• (a) Q gt 0, W 0
• (b) Q lt 0, W 0
• (c) Q 0, W gt 0
• (d) Q 0, W lt 0
• (e) Q gt 0, W gt 0
• (f) Q lt 0, W lt 0

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Work done when volume changes
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Work done when volume changes
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Work done when volume changes
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Work W is path-dependent

• W area under graph of the function p(V)
• W depends on initial and final states (1, 2)
• W depends on path taken (intermediate states)

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Q ( heat transferred) is also path-dependent
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Thermodynamic Concepts

• Thermodynamic systemdescribed by state
  variables (p, V, T, ..)
• Thermodynamic processchanges the state ( p, V,
  T, ...) of the system
• Heat Q, Work Wpath-dependent values depend
  on process

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Heat Q and Work W

• Q and W are not properties of the system
• (Q enters or leaves the system)
• (W is done on or by the system)
• We can measure the difference Q W
• Q W is related to a property of the system

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Q W

• We choose a thermodynamic system
• We take the system between a fixed initial final
  state for many different processes
• For each process, we measure Q W
• Experiment surprises us!

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Q W

• For this setup, we always find
• Q W has same value for all processes
• Q W depends only on initial, final state
• Q W is path-independent
• (these are three equivalent statements)

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Q W

• Since Q W depends only on state variables
• Q W a change in a property of the system
• We define U internal energy of system
• Q W DU

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First Law of Thermodynamics

• Q W DU
• or
• Q W DU
• Generalizes conservation of energy from just
  mechanical energy to include heat energy

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First Law of Thermodynamics

• Q W DU
• or
• Q W DU
• The heat energy Q added to a system goes into
  work W and change in internal energy U

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First Law of Thermodynamics

• Q W DU
• or
• Q W DU
• (Notation U is not simply potential energy)

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Laws of Thermodynamics

• Zeroth Law
• every thermodynamic system has a property called
  temperature T
• First Law DU Q W
• every thermodynamic system has a property called
  internal energy U

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DU Q W

• Recall
• Q can be gt 0, lt 0, 0
• W can be gt 0, lt 0, 0
• Thus
• DU can be gt 0, lt 0, 0

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Free Expansion

• Break partition
• Let gas expand freely into vacuum

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Free Expansion

• gas is in equilibrium at initial and final states
• gas is not in equilibrium between initial and
  final states

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Free Expansion

• Set-up for process Q 0 (insulation)W 0
  (no pushing)
• First Law saysDU Q W 0

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Free Expansion

• For the gas Dp , DV are nonzero
• Experiment shows
• low density (ideal) gases have DT 0 between
  initial and final states

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Free Expansion

• For the gas Dp , DV are nonzero
• Experiment DT 0
• First Law DU 0
• Conclude For an ideal gas, U only depends on T

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Laws of Thermodynamics

• Zeroth Law
• every thermodynamic system has a property called
  temperature T
• First Law DU Q W
• every thermodynamic system has a property called
  internal energy U

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First Law of Thermodynamics

• Q W DU
• or
• Q W DU
• Generalizes conservation of energy
• Heat energy Q added to a system goes into both
  work W and change in internal energy U

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Thermodynamic Processes

• Process Definition Consequence
• Free Expansion Q 0
• W 0 DU 0
• Cyclic closed loop DU 0
• Q 0 W

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Thermodynamic Processes

• Process Definition Consequence
• Isobaric p constant W p DV
• Isochoric V constant W 0 Q DU 0

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Thermodynamic Processes

• Process Definition Consequence
• Isothermal T constant DU 0
• (must be slow)
• Adiabatic Q 0 0 DU W
• (insulated or fast)

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Molar Heat Capacity Revisited

• Q n C DT
• Q energy needed to heat/cool n moles by DT
• CV molar heat capacity at constant volume
• Cp molar heat capacity at constant pressure

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CV for Ideal Gases, Revisited

• Molecular Theory
• (Ktot)av (f/2) nRT
• CV (f/2)R
• Monatomic f 3
• Diatomic f 3, 5, 7

• New language
• U (f/2) nRT
• CV (f/2)R
• Monatomic f 3
• Diatomic f 3, 5, 7

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Cp for Ideal Gases

• We expect
• Cp gt CV
• Example gas does work expanding against
  atmosphere
• We can show
• Cp CV R

Derive this result
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Cp for Ideal Gases

• monatomic gasCV (3/2)R
• diatomic gas at low T, CV (5/2)R

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Adiabatic Process (Q 0)

• An adiabatic process for an ideal gas obeys
• TV g -1 constant value
• pV g another constant

Derive these results
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Adiabatic Process (Q 0)

• For an ideal gas undergoing an adiabatic process

Derive these results
Derive some isobaric results
Do Problem 17-42