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PA2001: Time and Energy
Thermodynamics
• 0th Law
• Temperature scales
• The ideal gas• const. vol. thermometer
• 1st Law• Heat and Work• PV diagrams
Tipler Chapters 18,19,20
Thermodynamics 1
Dr Mervyn Roy, S6
PA2001: Time and Energy
Thermodynamics
• Thermodynamics = Thermal + Mechanical• Developed c. 19 – Steam Engines
• defined in terms of macroscopic properties of system – all can be determined by experiment.
Chemistry
Low temperature physics
Astrophysics
Propulsion
Powergeneration
PA2001: Time and Energy
Thermodynamics
0th Law
A B
no heat flow (adiabatic)
PA2001: Time and Energy
Thermodynamics
Eventually, A and B reach thermal equilibriumDefine – temperature
A B
A B
no heat flow (adiabatic)
0th Law: If 2 objects in thermal equilibrium with a 3rd, then they are in thermal equilibrium with each other
A C
B C
0th Law
PA2001: Time and Energy
Thermodynamics
Why bother?
1. Defines temperature (a universal property)
ma = mb ma = mc mb = mc
Universality is familiar…
PA2001: Time and Energy
Thermodynamics
1. Defines temperature (a universal property)
ma = mb ma = mc mb = mc
Lb = La La = Lc
Universality is familiar…
But not logically necessary,
but Lb ≠ Lca
b c
Why bother?
PA2001: Time and Energy
Thermodynamics
?
Temperature scales
Compare temperatures to invent a temperature scale.
Linear thermometer
L = Lo + T
Define using two fixed points (temperatures)
(eg. ice and boiling water)
PA2001: Time and Energy
Thermodynamics
Linear thermometer
L = Lo + T
Define using two fixed points (temperatures)
(Usually ice and boiling water)
Problems?
PA2001: Time and Energy
Thermodynamics
Ideal Gas
P V = n R Tn = no. of moles (1 mole = 6.02 x 10 23 molecules)R = universal gas constant (8.31 J / mol / K)
Equation of state of real gas ideal gas (c.17 onwards)Dilute real gasses are ideal – interaction between gas molecules is small
Solves one problem with the thermometer – linear variation with T.eg. at constant V, P directly proportional to T
PA2001: Time and Energy
Thermodynamics
Phase Diagram Water
SO
LID LIQUID
VAPOUR
Pressure (kPa)
Temperature (C)0.00 0.01 100.00
0.61
101
Triple point
normal melting pointnormal boiling point
T3 = 273.16 K
PA2001: Time and Energy
Thermodynamics
Constant volume gas thermometer
variable mercury reservoirsystem of unknown temp.(water for triple pt calibration)
bulb containing gas, P
h
rubber tube
P = (nr/V) TP = T
At triple point = P3 / T3
ThenT = (T3 / P3 ) P
PA2001: Time and Energy
Thermodynamics
Dilute gasses are more ‘ideal’
Van der Waals(P + a/V2) (V - b)=nRT
Ideal gas scale:
T = 273.16 (P / P3 )limP3
0
PA2001: Time and Energy
Thermodynamics
1st Law
Q = ΔU + WJust conservation of energy!
ΔUheat in work out
Internal energy changes
Q > 0 W > 0Equivalence of heat and mechanical energy (Joule c.19)
Revision:Q = c ΔTc = specific heat = amount of heat needed to raise 1 kg by 1 K
Eg. c (Au) = 0.126 KJ/Kg/K, c (H2O) = 4.18 KJ/Kg/K
PA2001: Time and Energy
Thermodynamics
PV diagrams
Work done by an ideal gas Work = Force x Distance
dx
AreaA
Gas
F
piston
P
VVi
Pf
Pi
P
V
Pi
Pf
Vi Vf
P
VVi Vf
Pi
PA2001: Time and Energy
Thermodynamics
P
VVi
Pf
Pi
P
V
Pi
Pf
Vi Vf
P
VVi Vf
Pi
ISOBAR ISOCHORR ISOTHERM
PV diagrams
PA2001: Time and Energy
Thermodynamics
dQ = dU + PdVIdeal gas: U = U(T)cp ≠ cv
cp - cv = nR
Q=WQ = ΔU = cvΔTQ = cpΔT = ΔU + PΔV
P
VVi Vf
Pi
ISOBAR P
VVi
Pf
Pi
ISOCHORR P
V
Pi
Pf
Vi Vf
ISOTHERM
1st Law
PA2001: Time and Energy
Thermodynamics
P
V
A
B
P
V
A
B
State variables, P, V, T, U
Always the same at A : PA, VA, TA, UA
Always the same at B : PB , VB, TB, UB
PV diagrams