Topic 2 Thermodynamics 1 Why Thermodynamics? • To tell us the relationship between the pp,ressure, temperature and density of a gas as it moves. • Altogether there are 6 variables we need to describe the state of a gas… • p pressure ()(Pa) • density (kg/m3), or specific volume v=1/ • T temperature (K) • e internal energy per unit mass ( ) • h enthalpy ( ), he+p/ • s entropy ( ) • To relate these variables we use 1. The Kinetic Theory of Gases, 2. The 1st Law of Thermodynamics, 3. Specific Heats 4. The 2nd Law of Thermodynamics 2 1. Kinetic Theory of Gases • Assumes • Gas is a collection of molecules in random motion • Molecules bounce of each other like hard spheres • Gives two sets of relations… Neglects forces between molecules Equation of State Gas constant R = 287 J/kg/K for air • Gases that obey these relations are called “Thermally Perfect” 3 Thermally Perfect • We will always assume gases are thermally perfect in this class, but this isn’t always true… Ceases to be valid at high densities. Why? 4 2. 1st Law of Thermodynamics “Energy is Conserved” W E Q W E Q Change in Amount of work Amount of energy done by pressure heat added and viscous forces Collection of identified Work = gas molecules (System) p V (<0) Surface area S 5 In terms of enthalpy… dq de pdv 6 3. Specific Heats • Specific heat – amount of heat needed to raise the q q temperature of 1kg by 1 Kelvin C • Two kinds: T T • Specific heat at constant volume Cv (q / T )v • Specific heat at constant pressure C p (q / T ) p Pratt and Whitney JT58 Test (Powered SR71)7 dq de pdv dq dh vdp With the energy equation… 8 de dh Cv Cp dT Calorically Perfect Gas dT A gas that is thermally perfect and for which the… • …specific heats are constant with temperature, so… • We will assume calorically perfect gases in this class, but… 9 4. 2nd Law of Thermodynamics Shock in a Converging Diverging Nozzle Bourgoing & Benay (2005), ONERA, France Schlieren visualization 10 Sensitive to in‐plane index of ref. gradient Processes and Entropy • Adiabatic Process ‐ no heat added or removed. • Reversible Process –no dissipative phenomena occur. • Isentropic Process – adiabatic and reversible Constant entropy. Entropy –measure of disorder in the gas molecules. • 2nd Law of Thermo – dissipative processes may only increase entropy, but adding or removing heat may increase or decrease entropy by an amount Q/T • So… 11 The Entropy Equation… For a reversible process… Tds dq 1st Law dq de pdv Therma lly de CvdT perfect gas p RT / v 12 C / C R C p Cv p v …The Entropy Equation 13 Isentropic Relations 1 s s T 2 1 log 2 1 C e T v 1 2 • If s2 – s1 = 0 then… 14 Summary Calorically All gases Thermally perfect perfect e e(T ) • p RT KTG h h(T ) dq de pdv st • 1 Law dq dh vdp C de / dT e C T • Specific Cv (e / T )v v v heats Cp (h / T ) p Cp dh / dT h CpT 1 nd s2 s1 T2 1 • 2 Law loge C T v 1 2 nd 1 • 2 Law 1 1 2 T2 p2 T2 Isentropic 1 T1 p1 T1 15.