Pressure-Volume Diagrams
Pressure-Volume Diagrams

Pressure-Volume Diagrams

Pressure-Volume Diagrams

math, math, math

Pressure-Volume Diagrams Recall from the previous section…

ΔU = Q + W

Q > 0 system absorbs heat from the environment
Q < 0 system releases heat to the environment
W > 0 work done on the system by the environment
W < 0 work done by the system on the environment

A system can be described by three thermodynamic variables — pressure, volume, and temperature. Well, maybe it’s only two variables. With everything tied together by the ideal gas law, one variable can always be described as dependent on the other two.







P = nRT
V
PV = nRT  ⇒ V = nRT
P
T = PV
nR

Temperature is the slave of pressure and volume on a pressure-volume graph (PV graph).

Function of State

ΔU = 3  nRΔT
2

Function of Path: Work

W = ∫ F · ds = ∫ P dV

W = − area on PV graph

Function of Path: Heat

Q = ΔU + W = ncΔT

cP = specific heat at constant pressure
cV = specific heat at constant volume

curves

  • isobaric
    • constant pressure
    • “bar” comes from the greek word for heavy: βαρύς [varys]
    • examples: weighted piston, flexible container in earth’s atmosphere, hot air balloon
    • PV graph is a horizontal line
    W = −PΔV  ⇒ ΔU = Q − PΔV

  • isochoric
    • constant volume
    • “chor” comes from the greek word for volume: χώρος [khoros]
    • examples: closed rigid container, constant volume thermometer
    • PV graph is a vertical line
    W = 0  ⇒ ΔU = Q

  • isothermal
    • constant temperature
    • “therm” comes from the greek work for heat: θερμότητα [thermotita]
    • examples: “slow” processes, breathing out through a wide open mouth
    • PV graph is a rectangular hyperbola
    ΔU = 0  ⇒ Q = −W

  • adiabatic
    • no heat exchange with the environment
    • adiabatic has a complex greek origin that means “not+through+go”: α + Δια + βατός [a + dia + vatos]
    • examples: “fast” processes, forcing air out through pursed lips, bicycle tire pump
    • PV diagram is a “steep hyperbola”
    Q = 0  ⇒ ΔU = W

    PVγ = constant

    γ = cP  = α + 1
    cV α
    3/2 + 1  = 5  monatomic
    3/2 3
    5/2 + 1  = 7  diatomic
    5/2 5

… and the rest

liquids

solids

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