Work in Thermodynamic Processes

1. Work in Thermodynamic Processes • Energy can be transferred to a system by heat and/or work • The system will be a volume of gas always in equilibrium • Consider a cylinder with a movable piston • As piston is pressed a distance Δy, work is done on the system reducing the volume  W = -F Δy = - P A Δy

2. Work in Thermodynamic Processes – Cont. • Work done compressing a system is defined to be positive • Since ΔV is negative (smaller final volume) & A Δy = V  W = - P ΔV • Gas compressed  Won gas = pos. • Gas expands  Won gas = neg.

3. Work in Thermodynamic Processes – Cont. • Can only be used if gas is under constant pressure • An isobaric process (iso = the same) P1 = P2 • Represented on a pressure vs. volume graph – a PV diagram • Area under any curve = work done on the gas • If volume decreases – work is positive (work is done on the system)

4. THERMODYNAMICS First Law of Thermodynamics • Energy is conserved • Heat added to a system goes into internal energy, work or both • ΔU = Q + W • Heat added to system  internal energy  Q is positive • Work done to the system  internal energy  W is positive (again)

5. First Law – Cont. • A system will have a certain amount of internal energy (U) • It will not have certain amounts of heat or work • These change the system • U depends only on state of system, not what brought it there • ΔU is independent of process path (like Ug)

6. Isothermal Process • Temperature remains constant • Since P = N kB T / V= constant / V • An isotherm (line on graph) is a hyperbola

7. Isothermal Process – Cont. • Moving from 1 to 2, temperature is constant, so P & V change • Work is done = area under curve • Internal energy is constant because temperature is constant  Q = -W • Heat is converted into mechanical work

8. Isometric (isovolumetric) Process • The volume is not allowed to change • V1 = V2 • Since no change in volume, no work is done  ΔU = Q • Heat added must go into internal energy  it • Heat extracted is at the expense of internal energy  it

9. Isometric Process – Cont. • The PV diagram representation • No change in volume • Area under curve = 0 • That is, no work done • The process moves from one isotherm to another

10. Isobaric Process • As heat is added to system, pressure is required to be constant • The ratio of V / T = constant • Some of the heat does work and the rest causes a change in temperature • Thus moving to another isotherm • Recall: changes in temperature = changes in internal energy  ΔU = Q + W

11. Adiabatic Process • No heat is transferred into or out of system • Q = 0  ΔU = W • All work done to a system goes into internal energy increasing temperature • All work done by the system comes from internal energy & system gets cooler

12. Adiabatic Process – Cont. • Either system is insulated to not allow heat exchange or the process happens so fast there is no time to exchange heat

13. Adiabatic Process – Cont. • Since temperature changes, we move isotherms

14. The Second Law of Thermodynamics & Heat Engines • Heat will not flow spontaneously from a colder body to a warmer • OR: Heat energy cannot be transferred completely into mechanical work • OR: It is impossible to construct an operational perpetual motion machine

15. Heat Engines • Any device that converts heat energy into work • Takes heat from a high temperature source (reservoir), converts some into work, then transfers the rest to surroundings (cold reservoir) as waste heat

16. Heat Engines – Cont. • Consider a cylinder and piston • Surround by water bath & allow to expand along an isothermal • The heat flowing in (Q) along AC equals the work done by the gas as it expands (W) since ΔU = 0 • To return to A along same isothermal, work is done on the gas and heat flows out • Work expanding = work compressing

17. Heat Engines – Cont. • A cycle naturally can have positive work done • In going from A to B work is done by gas, temperature  (ΔU ) and heat enters system • B to C • No work done, T , ΔU , & heat leaves system • C to A • ΔU = 0, heat leaving = work done • The work out = the net heat in (ΔU = 0)

18. Heat Engines – Cont. • Thermal Efficiency • Used to rate heat engines • efficiency = work out / heat in  e = Wout / Qin • Qin = heat into heat engine • Qout = heat leaving heat engine • For one cycle, energy is conserved  Qin = W + Qout • Since system returns to its original state ΔU = 0

21. The Carnot Engine • Any cyclic heat engine will always lose some heat energy • What is the maximum efficiency? • Solved by Sadi Carnot (France) (Died at 36) • Must be reversible adiabatic process

22. The Carnot Engine – Cont. • Carnot Cycle • A four stage reversible process • 2 isotherms & 2 adiabats • Consider a hypothetical device – a cylinder & piston • Can alternately be brought into contact with high or low temperature reservior • High temp – heat source • Low temp – heat sink – heat is exhausted

23. The Carnot Engine – Cont. • Step 1: an isothermal expansion, from A to B • Cylinder receives heat from source • Step 2: an adiabatic expansion, from B to C

24. The Carnot Engine – Cont. • Step 3: an isothermal compression, C to D • Ejection of heat to sink at low temp • Step 4: an adiabatic compression, D to A • Represents the most efficient (ideal) device • Sets the upper limit

26. Entropy • A measure of disorder • A messy room > neat room • Pile of bricks > building made from them • A puddle of water > ice came from • All real processes increase disorder  increase entropy •  of entropy of one system can be reduced at the expense of another

27. Entropy – Cont. • Entropy of the universe always increases • The universe only moves in one direction – towards  entropy • This creates a “direction of time flow” • Nature does not move systems towards more order

28. Entropy – Cont. • As entropy , energy is less able to do work • The “quality” of energy has been reduced • Energy has “degraded” • Nature proceeds towards what is most likely to happen