Thermodynamics

First Law of Thermodynamics Energy Conservation  U = Q - W Heat flow into system Increase in internal energy of system Work done by system V P V 1 V 2 P1P3P1P3 Equivalent ways of writing 1st Law: Q =  U + W The change in internal energy of a system (  U) is equal to the heat flow into the system (Q) minus the work done by the system (W) 07

Work Done by a System M M yy W = p  V :For constant Pressure W > 0 if  V > 0 expanding system does positive work W < 0 if  V < 0 contracting system does negative work W = 0 if  V = 0 system with constant volume does no work W = F d cos  =P A d = P A  y = P  V 13 The work done by the gas as it contracts is A) PositiveB) ZeroC) Negative

Thermodynamic Systems and P-V Diagrams l ideal gas law: PV = nRT l for n fixed, P and V determine “state” of system è T = PV/nR è U = (3/2)nRT = (3/2)PV l Examples: è which point has highest T? » è which point has lowest U? »to change the system from C to B, energy must be added to system V P A B C V 1 V 2 P1P3P1P3 17

Special PV Cases l Constant Pressure (isobaric) l Constant Volume (isochoric) Constant Temp  U = 0 l Adiabatic Q=0 V P W = P  V (>0)  V > 0V P W = P  V =  V = 0 42

First Law of Thermodynamics Isobaric Example V P 1 2 V 1 V 2 P 2 moles of monatomic ideal gas is taken from state 1 to state 2 at constant pressure p=1000 Pa, where V 1 =2m 3 and V 2 =3m 3. Find T 1, T 2,  U, W, Q. (R=8.31 J/k mole) 21

First Law of Thermodynamics Isochoric Example 2 moles of monatomic ideal gas is taken from state 1 to state 2 at constant volume V=2m 3, where T 1 =120K and T 2 =180K. Find Q. V P 2 1 V P2P1P2P1 24

Example: complete cycle V P V P W = P  V (>0)  V > 0V P W = P  V =  V = 0 V P W = P  V (<0)  V < 0 V W = P  V = P  V = 0 V P W tot > 0 W tot = ?? 27

WORK Question If we go the opposite direction for the cycle (4,3,2,1) the net work done by the system will be A) PositiveB) Negative V P If we go the other way then 30

PV Question Shown in the picture below are the pressure versus volume graphs for two thermal processes, in each case moving a system from state A to state B along the straight line shown. In which case is the work done by the system the biggest? A. Case 1 B. Case 2 C. Same A B V(m 3 ) Case 1 A B V(m 3 ) P(atm) Case 2 P(atm) Net Work = area under P-V curve Area the same in both cases! 29

PV Question2 Shown in the picture below are the pressure versus volume graphs for two thermal processes, in each case moving a system from state A to state B along the straight line shown. In which case is the change in internal energy of the system the biggest? A. Case 1 B. Case 2 C. Same A B V(m 3 ) Case 1 A B V(m 3 ) P(atm) Case 2 P(atm)  U = 3/2  (pV) Case 1:  (pV) = 4x9-2x3=30 atm-m 3 Case 2:  (pV) = 2x9-4x3= 6 atm-m 3 31

PV Question3 Shown in the picture below are the pressure versus volume graphs for two thermal processes, in each case moving a system from state A to state B along the straight line shown. In which case is the heat added to the system the biggest? A. Case 1 B. Case 2 C. Same A B V(m 3 ) Case 1 A B V(m 3 ) P(atm) Case 2 P(atm) Q =  U + W W is same for both  U is larger for Case 1 Therefore, Q is larger for Case 1 34

Q =  U + W Heat flow into system Increase in internal energy of system Work done by system V P V 1 V 2 P1P3P1P3 Which part of cycle has largest change in internal energy,  U ? 2  3 (since U = 3/2 pV) l Which part of cycle involves the least work W ? 3  1 (since W = p  V) l What is change in internal energy for full cycle?  U = 0 for closed cycle (since both p & V are back where they started) l What is net heat into system for full cycle (positive or negative)?  U = 0  Q = W = area of triangle (>0) Some questions: First Law Questions 37

Question Consider a hypothetical device that takes 1000 J of heat from a hot reservoir at 300K, ejects 200 J of heat to a cold reservoir at 100K, and produces 800 J of work. Does this device violate the first law of thermodynamics ? 1. Yes 2. No l W (800) = Q hot (1000) - Q cold (200) l Efficiency = W/Q hot = 800/1000 = 80% 45

Reversible? l Most “physics” processes are reversible, you could play movie backwards and still looks fine. (drop ball vs throw ball up) l Exceptions: è Non-conservative forces (friction) è Heat Flow: »Heat never flows spontaneously from cold to hot 47

Summary: è 1st Law of Thermodynamics: Energy Conservation Q =  U + W Heat flow into system Increase in internal energy of system Work done by system V P l point on p-V plot completely specifies state of system (pV = nRT) l work done is area under curve l U depends only on T (U = 3nRT/2 = 3pV/2) for a complete cycle  U=0  Q=W 50