Chapter 17 The First Law of Thermodynamics Thermodynamic
- Slides: 41
Chapter 17 The First Law of Thermodynamics
Thermodynamic Concepts • Thermodynamic system: able to exchange heat with its surroundings • State variables: p, V, T, . . . describe 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
thermodynamic system: can exchange heat with its surroundings state of system: (p, V, T, . . . ) thermodynamic process: changes state of the system
thermodynamic process: 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
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 = n. C 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)
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 Free Expansion: Cyclic: Definition Q=0 W=0 closed loop Consequence 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 (must be slow) DU = 0 Adiabatic Q=0 (insulated or fast) 0 = DU + W
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) n. RT CV = (f/2)R Monatomic: f = 3 Diatomic: f = 3, 5, 7 New language: U = (f/2) n. RT 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 p. V 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
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