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