# Thermodynamics (in a nutshell)

## First Law of Thermodynamics

### Important terms

Work done on system, W. Work is computed by original definition: the component of force moving through a distance. Examples in internal combustion engine.

• Crankshaft pushes piston in cylinder to compress gas; increases energy of system.
• Expanding combusted gas pushes cylinder out; decreases energy of system.

Heat absorbed by system, Q. Examples in internal combustion engine.

• Ignited fuel heats system; increasing temperature.
• Cold fuel injected; decreasing temperature

First Law. Energy of system U -- the sum of work done on system W and heat absorbed by system Q -- is conserved, that is, U = W + Q is conserved.

## Ideal Engine (Carnot cycle)

 Heat QH > 0 added at constant TH. Piston moves out: WH < 0 . (1→2) Energy conserved: QH+WH=QL+WL. Work done by system W =WL-WH=QH-QL Hence QH=W+QL.

## Efficiency

Reviewing steps in which we ignore work change during heating and cooling and heat changes during work in or work out. In other words, we assume energy is conserved in actual engine.

1. Increases thermal energy QH at high temperature TH
2. Exhausts thermal energy QL at low temperature TL
3. Does work W given by energy conservation:
QH = W + QL.

The efficiency is the work done (W) compared to the total energy input QH.
 Efficiency = W/ QH (definition) = (QH- QL)/QH (Thermo 1st law; conservation of energy = 1- QL/QH = 1 - TL/TH Q ∝T (coming attraction)

### On the web

• (+ realistic cycles);

### Heat Pump and Refrigerator

See examples of animated Carnot and Rankine cycles and layout of Otto cycle.

## Chosing the Fluid for Engine

In examples above, we used "ideal gas" but many engines used different fluids to optimize performance. In our ideal engine we imagined increasing energy at constant high temperature or removing energy at constant low temperature. (Both impossible of course.) The latent heat is central to picking best fluid.

### Latent Heat of water

When a material changes phase -- e.g., ice to water or water to steam -- extra energy is required to convert one 1 kg from one phase into another. These are called Latent Heat of Fusion or Latent Heat of Evaporation, respectively. Fusion Water Mercury Sulfur Nitrogen

If added 1 kg of ice at 0 C to 10 kg of water at 10 C, what is temperature of final mixture?

Ice will melt and form 11 kg of water. The specific heat of water is 4.2 kJ/kg.
345=(10+1)*(10-T)*4.2 or T = 10 - 345/11./4.2 = 2.5 C.
For water at 20 C (68 F), 3 parts ice, lower temperature to 1 C.

## Thermodynamics & Reality

### Review

Work, W, is that done to system.
But for efficiency use Wdone by system.

Heat, Q, is heat added to system.

Energy = W + Q is conserved: Thermo. 1st Law

Engine transfers heat energy into work (e.g., internal combustion engines) or work into heat transfer (e.g., refrigerator or heat pump).

Efficiency of heat engine is Wdone/Qhot, in other words, work done compared to total heat input.

Conservation of energy, Wdone = Qhot- Qcold, then efficiency = Wdone/Qhot = 1 - Qcold/Qhot < 1.

heat pumps, enthusiastic sales staff typically use
coefficient of performance = (heat out)/(work done),
that is, CP=Qhot/(Qhot- Qcold) > 1.

## Temperature: Connection to Heat

Kelvin found absolute scale of temperature, Kelvin (K). Nothing can be colder. (0 K = -273 C = -459 F).

Kinetic energy. In an ideal gas, average energy of any molecule is (3/2) kb T. Here kb is a (Boltzmann) constant so kbT in joules.

In an engine driven by an ideal gas, the energy transferred is the difference in the kinetic energy.
Qhot- Qcold ∝ Thot- Tcold.

### Heat Capacity

In any material, over small temperature change (ΔT), thermal energy change (ΔQ) is proportional to temperature, connected by
specific heat capacity C: ΔQ = C ΔT.

Typical value of heat capacity. (Water conspiracy)

One calorie heats 1 gram of water 1 degree C.
Heat capacity of water 1 cal/g-C = 4.2 kJ/kg-C is typical of many materials, namely kJ/kg-C.

### Heat Flow from High to Low Temperature

• Conduction is heat transfer in material; TH → TL. E.g., pan on stove; inside window in cold weather.

• Convection is heat carried by moving fluid.
E.g., steam heat on campus; chilled water also?

• Radiation is heat transfer without material.
E.g., sun; laser heating (are sources hotter?).

### Entropy Definitions (sneaked past you)

1. Thermodynamic entropy S. For a closed thermodynamic system, amount of thermal energy unavailable to do work.

2. A measure of the disorder in a closed system.

3. information loss in transmitted message.

4. The tendency for matter/energy in the universe to evolve toward a state of inert uniformity.

## Second Law of Thermo. Losing game.

Alternate statements:

In closed system, available thermal energy to do work can never be completely used.

Since entropy is thermal energy unavailable to do work; in closed system entropy can never decrease.

For closed universe, its entropy increases (Clausius).

### Implications for Efficiency

Definition: Wdone/QH.

First Law: QH = W + QL.
efficiency = (QH - QL)/QH = 1 - QL/QH.

Thermal energy is proportional to temperature.
efficiency =1 - TL/TH < 1.

Second Law. W < QH - QL.
efficiency < 1 - TL/TH

## Reality

First law: can't use all heat input for work, only net.
Second law: can't use all the net heat. Really can't win.
The smaller TL/TH the better.

### Turbine engines

For tri-class seating with 250 seats, 3000 mile flight, the relative fuel consumption per trip has dramatically improved. At the introduction of each: (current four-engine)/(current two engine)/7E7: 2.4/2.0/1.0!

Changes in first-law efficiency. Based on using turbine exit for high temperature and compressor exit for low temperature. Fahrenheit Kelvin Year TL 1970 1994 2024

 Year 1978 1980 1990 2000 2005 2007 MPG (RT) 2.9 3.1 3.8 4.9 5.8 6.1

Short history of development of thermodynamics.