1. PA2001: Time and Energy Thermodynamics 0 th Law Temperature scales The ideal gas const. vol. thermometer 1 st Law Heat and Work PV diagrams Tipler Chapters 18,19,20 Thermodynamics 1 Dr Mervyn Roy, S6

2. 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 Power generation

3. PA2001: Time and Energy Thermodynamics 0 th Law AB no heat flow (adiabatic)

4. PA2001: Time and Energy Thermodynamics Eventually, A and B reach thermal equilibrium Define – temperature AB AB no heat flow (adiabatic) 0 th Law: If 2 objects in thermal equilibrium with a 3 rd, then they are in thermal equilibrium with each other ACBC 0 th Law

5. PA2001: Time and Energy Thermodynamics Why bother? 1.Defines temperature (a universal property) m a = m b m a = m c m b = m c Universality is familiar…

6. PA2001: Time and Energy Thermodynamics 1.Defines temperature (a universal property) m a = m b m a = m c m b = m c L b = L a L a = L c Universality is familiar… But not logically necessary, but L b ≠ L c a bc Why bother?

7. PA2001: Time and Energy Thermodynamics ? Temperature scales Compare temperatures to invent a temperature scale. Linear thermometer L = L o +  T Define  using two fixed points (temperatures) (eg. ice and boiling water)

8. PA2001: Time and Energy Thermodynamics Linear thermometer L = L o +  T Define  using two fixed points (temperatures) (Usually ice and boiling water) Problems?

9. PA2001: Time and Energy Thermodynamics Ideal Gas P V = n R T n = 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

10. PA2001: Time and Energy Thermodynamics Phase Diagram Water SOLID LIQUID VAPOUR Pressure (kPa) Temperature (C) 0.000.01 100.00 0.61 101 Triple point normal melting point normal boiling point T 3 = 273.16 K

11. PA2001: Time and Energy Thermodynamics Constant volume gas thermometer variable mercury reservoir system of unknown temp. (water for triple pt calibration) bulb containing gas, P h rubber tube P = (nr/V) T P =  T At triple point  = P 3 / T 3 Then T = (T 3 / P 3 ) P

12. PA2001: Time and Energy Thermodynamics Dilute gasses are more ‘ideal’ Van der Waals (P + a/V 2 ) (V - b)=nRT Ideal gas scale: T = 273.16 (P / P 3 ) lim P30P30

13. PA2001: Time and Energy Thermodynamics 1 st Law Q = ΔU + W Just conservation of energy! ΔUΔU heat in work out Internal energy changes Q > 0 W > 0 Equivalence of heat and mechanical energy (Joule c.19) Revision: Q = c ΔT c = specific heat = amount of heat needed to raise 1 kg by 1 K Eg. c (Au) = 0.126 KJ/Kg/K, c (H 2 O) = 4.18 KJ/Kg/K

14. PA2001: Time and Energy Thermodynamics PV diagrams Work done by an ideal gas Work = Force x Distance dx Area A Gas F piston P V ViVi PfPf PiPi P V PiPi PfPf ViVi VfVf P V ViVi VfVf PiPi

15. PA2001: Time and Energy Thermodynamics P V ViVi PfPf PiPi P V PiPi PfPf ViVi VfVf P V ViVi VfVf PiPi ISOBAR ISOCHORRISOTHERM PV diagrams

16. PA2001: Time and Energy Thermodynamics dQ = dU + PdV Ideal gas: U = U(T) c p ≠ c v c p - c v = nR Q=WQ = ΔU = c v ΔTQ = c p ΔT = ΔU + PΔV P V ViVi VfVf PiPi ISOBAR P V ViVi PfPf PiPi ISOCHORR P V PiPi PfPf ViVi VfVf ISOTHERM 1 st Law

17. PA2001: Time and Energy Thermodynamics P V A B P V A B State variables, P, V, T, U Always the same at A : P A, V A, T A, U A Always the same at B : P B, V B, T B, U B PV diagrams