The First Law of Thermodynamics Chapter 17 The First Law of Thermodynamics

Thermodynamic Concepts Thermodynamic system: able to exchange heat with its surroundings State variables: p, V, T, ... describe the thermodynamic system Thermodynamic process: changes the state ( p, V, T, ...) of the system

Thermodynamic Process Heat Q: can leave or enter system Work W: system can do work on its surroundings surroundings can do work on the system

thermodynamicsystem: can exchange heat with its surroundings state of system: (p, V, T, ...) thermodynamicprocess: changes state of the system

thermodynamicprocess: changes state of the system We’ll focus on the roles of: Heat Q Work W

Heat Q: can leave or enter system Q > 0: heat added to system Q < 0: heat removed from system

Q > 0: heat added to system Sign Conventions for Q Q > 0: heat added to system Q < 0: heat removed from system Consistent with sign of DT from earlier: Q = mc DT or Q = nC DT

Work W: W > 0: system does work on its surroundings W < 0: surroundings does work on the system

Sign Conventions for W W > 0: system does work on surroundings W < 0: surroundings does work on system (the ‘opposite perspective’ as in mechanics)

(a) Q > 0, W = 0 (b) Q < 0, W = 0 (c) Q = 0, W > 0 (d) Q = 0, W < 0 (e) Q > 0, W > 0 (f) Q < 0, W < 0

Work done when volume changes

Work done when volume changes

Work done when volume changes

Work W is path-dependent W = area under graph of the function p(V) W depends on initial and final states (1, 2) W depends on path taken (intermediate states)

Q (= heat transferred) is also path-dependent

Thermodynamic Concepts Thermodynamic system: described by state variables (p, V, T, ..) Thermodynamic process: changes the state ( p, V, T, ...) of the system Heat Q, Work W: ‘path-dependent’: values depend on process

Heat Q and Work W Q and W are not properties of the system (Q enters or leaves the system) (W is done on or by the system) We can measure the difference: Q – W Q – W is related to a property of the system

Q – W We choose a thermodynamic system We take the system between a fixed initial final state for many different processes For each process, we measure Q – W Experiment surprises us!

Q – W For this setup, we always find: Q – W has same value for all processes Q – W depends only on initial, final state Q – W is path-independent (these are three equivalent statements)

Q – W Since Q – W depends only on state variables: Q – W = a change in a property of the system We define U = ‘internal energy’ of system: Q – W = DU

First Law of Thermodynamics Q – W = DU or Q = W + DU Generalizes conservation of energy from just mechanical energy to include heat energy

First Law of Thermodynamics Q – W = DU or Q = W + DU The heat energy Q added to a system goes into work W and change in internal energy U

First Law of Thermodynamics Q – W = DU or Q = W + DU (Notation: U is not simply ‘potential energy’)

Laws of Thermodynamics Zeroth Law: ‘every thermodynamic system has a property called temperature T’ First Law: DU = Q – W ‘every thermodynamic system has a property called internal energy U’

DU = Q – W Recall: Q can be > 0, < 0, = 0 W can be > 0, < 0, = 0 Thus: DU can be > 0, < 0, = 0

Free Expansion Break partition Let gas expand freely into vacuum

Free Expansion gas is in equilibrium at initial and final states gas is not in equilibrium between initial and final states

Free Expansion Set-up for process: Q = 0 (insulation) W = 0 (no pushing) First Law says: DU = Q – W = 0

Free Expansion For the gas: Dp , DV are nonzero Experiment shows: low density (‘ideal’) gases have DT = 0 between initial and final states

Free Expansion For the gas: Dp , DV are nonzero Experiment: DT = 0 First Law: DU = 0 Conclude: For an ideal gas, U only depends on T

Laws of Thermodynamics Zeroth Law: ‘every thermodynamic system has a property called temperature T’ First Law: DU = Q – W ‘every thermodynamic system has a property called internal energy U’

First Law of Thermodynamics Q – W = DU or Q = W + DU Generalizes conservation of energy: Heat energy Q added to a system goes into both work W and change in internal energy U

Thermodynamic Processes Process Definition Consequence Free Expansion: Q = 0 W = 0 DU = 0 Cyclic: closed loop DU = 0 Q = 0 + W

Thermodynamic Processes Process Definition Consequence Isobaric p = constant W = p DV Isochoric V = constant W = 0 Q = DU + 0

Thermodynamic Processes Process Definition Consequence Isothermal T = constant DU = 0 (must be slow) Adiabatic Q = 0 0 = DU + W (insulated or fast)

Molar Heat Capacity Revisited Q = n C DT Q = energy needed to heat/cool n moles by DT CV = molar heat capacity at constant volume Cp = molar heat capacity at constant pressure

CV for Ideal Gases, Revisited Molecular Theory: (Ktot)av = (f/2) nRT CV = (f/2)R Monatomic: f = 3 Diatomic: f = 3, 5, 7 New language: U = (f/2) nRT CV = (f/2)R Monatomic: f = 3 Diatomic: f = 3, 5, 7

Cp for Ideal Gases We expect: Cp > CV Example: gas does work expanding against atmosphere We can show: Cp = CV + R Derive this result

Cp for Ideal Gases monatomic gas: CV = (3/2)R diatomic gas: at low T, CV = (5/2)R

Adiabatic Process (Q = 0) An adiabatic process for an ideal gas obeys: TV g -1 = constant value pV g = another constant Derive these results

Adiabatic Process (Q = 0) For an ideal gas undergoing an adiabatic process: Derive these results Derive some isobaric results Do Problem 17-42