2 Thermodynamic Systems, States and Processes Objectives are to:define thermodynamics systems and states of systemsexplain how processes affect such systemsapply the above thermodynamic terms and ideas to the laws of thermodynamics
3 At room temperature, for most gases: Internal Energy of a Classical ideal gas“Classical” means Equipartition Principle applies: each molecule has average energy ½ kT per in thermal equilibrium.At room temperature, for most gases:monatomic gas (He, Ne, Ar, …)3 translational modes (x, y, z)diatomic molecules (N2, O2, CO, …)3 translational modes (x, y, z)+ 2 rotational modes (wx, wy)Note: At higher temps, other modes can come in, e.g., vibrational modes.
4 Internal Energy of a Gas A pressurized gas bottle (V = 0.05 m3), contains helium gas (an ideal monatomic gas) at a pressure p = 1×107 Pa and temperature T = 300 K. What is the internal thermal energy of this gas?
5 Changing the Internal Energy U is a “state” function --- depends uniquely on the state of the system in terms of p, V, T etc.(e.g. For a classical ideal gas, U = NkT )There are two ways to change the internal energy of a system:WORK done by the system on the environmentWby = -WonHEAT is the transfer of thermal energy into the system from the surroundingsQThermal reservoirWork and Heat are process energies, not state functions.
6 Work Done by An Expanding Gas The expands slowly enough tomaintain thermodynamic equilibrium.Increase in volume, dV+dV Positive Work (Work isdone by the gas)-dV Negative Work (Work isdone on the gas)
7 A Historical Convention +dV Positive Work (Work isdone by the gas)-dV Negative Work (Work isdone on the gas)Energy leaves the systemand goes to the environment.Energy enters the systemfrom the environment.
8 Total Work Done To evaluate the integral, we must know how the pressure depends (functionally)on the volume.
9 Pressure as a Function of Volume Work is the area underthe curve of a PV-diagram.Work depends on the pathtaken in “PV space.”The precise path serves to describe the kind of process that took place.
10 Different Thermodynamic Paths The work done depends on the initial and finalstates and the path taken between these states.
11 Work done by a Gas dWby = F dx = pA dx = p (A dx)= p dV dx When a gas expands, it does work on its environmentConsider a piston with cross-sectional area A filled with gas. For a small displacement dx, the work done by the gas is:dxdWby = F dx = pA dx = p (A dx)= p dVWe generally assume quasi-static processes (slow enough that p and T are well defined at all times):This is just the area under the p-V curveVppVpVNote that the amount of work needed to take the system from one state to another is not unique! It depends on the path taken.
12 What is Heat?Up to mid-1800’s heat was considered a substance -- a “caloric fluid” that could be stored in an object and transferred between objects. After 1850, kinetic theory.A more recent and still common misconception is that heat is the quantity of thermal energy in an object.The term Heat (Q) is properly used to describe energy in transit, thermal energy transferred into or out of a system from a thermal reservoir …(like cash transfers into and out of your bank account)QUQ is not a “state” function --- the heat depends on the process, not just on the initial and final states of the systemSign of Q : Q > 0 system gains thermal energyQ < 0 system loses thermal energy
13 An Extraordinary Fact The work done depends on the initial and final states and the path taken between these states.BUT, the quantity Q - W does not dependon the path taken; it depends only on the initialand final states.Only Q - W has this property. Q, W, Q + W,Q - 2W, etc. do not.So we give Q - W a name: the internal energy.
14 The First Law of Thermodynamics (FLT) -- Heat and work are forms of energy transfer and energy is conserved.U = Q + Wonchange intotal internal energyheat addedto systemwork doneon the systemState Function Process FunctionsorU = Q - Wby
15 1st Law of Thermodynamics statement of energy conservation for a thermodynamic systeminternal energy U is a state variableW, Q process dependent
16 The First Law of Thermodynamics What this means: The internal energy of a systemtends to increase if energy is added via heat (Q)and decrease via work (W) done by the system.. . . and increase via work (W) done on the system.
17 Isoprocessesapply 1st law of thermodynamics to closed system of an ideal gasisoprocess is one in which one of the thermodynamic (state) variables are kept constantuse pV diagram to visualise process
18 Isobaric Processprocess in which pressure is kept constant
19 Isochoric Processprocess in which volume is kept constant
20 Isothermal Processprocess in which temperature is held constant
21 Thermodynamic processes of an ideal gas ( FLT: DU = Q - Wby ) Isochoric (constant volume)Vp12QTemperature changesFLT:Isobaric (constant pressure)Vp12FLT:QTemperature and volume change
22 Isothermal (constant temperature) ( FLT: DU = Q - Wby )Isothermal (constant temperature)QThermal ReservoirTVolume and pressure changepV12FLT: