1

Outline • • • • Define terms and conventions Introduce 1 st law of thermodynamics Contrast state and non-state properties Describe the Carnot cycle 2

System and environment • • • • System = what we wish to study – View as control mass or control volume Control mass (CM) – Define some mass, hold fixed, follow it around Control volume (CV) – Define and monitor a physical space Environment = everything else that may interact with the system 3

System states • • Systems may be open or closed to mass – Open systems permit mass exchange across system boundaries – Our CVs are usually open – Strictly speaking, a CM is closed Closed systems may be isolated or nonisolated – Isolated systems do not permit energy transfer with environment – Closed, isolated system = environment doesn’t matter 4

Lagrangian vs. Eulerian • • CM is the Lagrangian viewpoint – Powerful, desirable but often impractical – Total derivatives – Freeway example CV is the Eulerian viewpoint – Observe flow through volume – Partial derivatives 5

Air parcel • • • Our most frequently used system CM (usually!) – Lagrangian concept Monitor how T, p, and V change as we follow it around 6

Conventions • • • We often use CAPITAL letters for extensive quantities, and lower case for specific quantities – Specific = per unit mass Example: – U is internal energy, in Joules – – u is specific internal energy, in J/kg Unfortunately, “u” is also zonal wind velocity Exceptions: – Temperature T is essentially specific, but capitalized (and isn’t per unit mass anyway) – Pressure p is fundamentally extensive, but lower case 7

Energy and the 1 st law • • • • Total energy = KE + PE + IE – Conserved in absence of sources and sinks Our main use of 1 internal energy (IE or u) owing to sources and sinks st law: monitor changes in How do we change system u? With energy transfer via – heat Q or q – work W or w Caveat: w is also vertical velocity, and q will be reused (briefly) for water vapor specific humidity 8

Work • • Work = force applied over a distance – Force: N, distance: m – Work: Nm = J = energy Our principal interest: CM volume compression or expansion (dV) in presence of external pressure (p) • W > 0 if dV > 0 9

Work

W > 0 when system expands against environment

10

Heat • • Diabatic heat – Diabatic: Greek for “passable, to be passed through” – Internal energy exchanged between system and environment – q > 0 when energy flow is INTO system Adiabatic = system is isolated – Adiabatic: impassable, not to be passed through 11

Caution on nomenclature • • • • We should use diabatic when the energy exchange is between system and environment But, what if the heat source or sink is inside the system?

– That’s adiabatic, but q ≠ 0 – Our interior heat source will be water changing phase Dry adiabatic: q = 0 – No heat source, outside OR inside – “dry” really means no water phase changes Moist adiabatic: q ≠ 0, but heat source/sink is inside system – “moist” implies water phase change – Synonyms include “saturated adiabatic” and “wet adiabatic” – Can also be referred to as “diabatic”!

12

1 st law • In the absence of ∆KE and ∆PE • Other ways of writing this Most of my examples will be per unit mass.

13

State properties • • Internal energy u is a state property Changes in state properties are not path dependent • Other state properties include m, T, p, r , V, etc.

14

State properties 15

Path-dependence • Work and heat are path-dependent 16

Path-dependence • A cyclic process starts and ends with the same state property values • … but the cyclic process can have net heat exchange and do net

work

17

Path-dependence 18

Path-dependence 19

Carnot cycle • • • • • 4-step piston cycle on a CM 2 steps of volume expansion, 2 of volume compression 2 steps are isothermal, 2 are (dry) adiabatic Warm and cold thermal reservoirs external to system Start and end with temperature T 1 volume V 1 and 20

Carnot – Step 1

Isothermal volume expansion

Add heat Q A reservoir from warm T 2 V 2 = T 1 > V 1 21

Carnot – Step 2

Adiabatic volume expansion

No heat exchange T 3 V 3 < T 2 > V 2 22

Carnot – Step 3

Isothermal volume compression

Lose heat Q B reservoir to cold thermal T 4 V 4 = T 3 < V 3 23

Carnot – Step 4

Adiabatic volume compression

No heat exchange T 1 V 1 > T 4 < V 4

Returned to original state T 1 , V 1 .

Cycle is complete.

24

25

Apply 1 st law 26

Carnot on T-V diagram 27

Carnot on T-V diagram 28

Carnot on T-V diagram 29

Carnot on T-V diagram 30

Carnot on T-V diagram 31

Carnot on T-V diagram 32

Carnot on T-V diagram

No net ∆V But did net W

33

Conceptual summary

Heat flow diverted to do work

34

Question for thought #1

The isothermal expansion (Q A ) occurred at a higher temperature than the Isothermal compression (Q B ). What does this imply for the work?

Q B is waste heat.

What does this imply for the efficiency of this heat engine?

Is there a limit to efficiency?

Is the limit found in the 1 st law?

35

Question for thought #2 Can you design a cyclic process that does no net work? What would it look like on a T-V diagram?

36

Summary • • • 1 st law says, in essence, if you can’t take the heat, you can’t do the work Work and heat are path-dependent Carnot cycle illustrates isothermal and (dry) adiabatic processes – Heat diverted to do work, but some is wasted W = Q A - Q B 37