"Heat" Engines

A heat engine is a device that uses thermal energy in some form, converting some of it into mechanical energy (KineticE) in a cyclic process.

Efficiency of heat engines

Just like any other energy transformation, a portion of the input energy goes to...ThermalE.

What's the efficiency of the cartoon heat engine shown?

energy efficiency = $\frac{W o r k_{out}}{ThermalE_{i n}}$

Example
What is the efficiency of generating electricity from all energy sources in this country?

What is the efficiency of transportation in this country?

Second Law of Thermodynamics - Heat engines

The law of heat engines is another way of stating the second law...

Any cyclic process that uses thermal energy to do work must also have a thermal energy exhaust: Heat engines are always less than 100% efficient at using thermal energy to do work.

Heat engine efficiencies

heat engine efficiencies

There is a pattern to be found here, for how the efficiency depends on $T_{in}$ and $T_{exhaust}$. Examine the table, and see if you can see it...

 

 

 

 

Absolute temperatures

For a gas of identical atoms, each with mass $m$: $$k_bT=\frac 12 m \myc {v^2}$$

"Absolute zero" is -273 C. But how can you have negative temperatures?

The temperature in the equations is "absolute temperature", measure from absolute zero.

  • -273 C = 0 K, where "K" means "Kelvin degrees above absolute zero".
  • The size of a kelvin and celsius degree are the same.
  • So 0 C = ____ K?
  • Room temperature ~25 C = ______ K?
  • 400 C = ______ K?

Maximum efficiency of heat engines

Using absolute temperatures (measured from absolute zero), it turns out that the 2nd law determines the maximum efficiency of any heat engine to be related to the temperatures at which it operates:

$$\text{ efficiency}_{max} =\frac{T_{Hot}-T_{Cold}}{T_{Hot}}= 1-T_{Cold}/T_{Hot}.$$

So the theoretical best (e.g. no engine friction...) you could do with a gasoline engine is... $$\text{eff}_\text{max} = 1-T_{cold}/T_{hot}=1-298/673=0.557 = 56\%.$$ (actually they're about 25% efficient).

So...how could you change a gas engine to be more efficient (and thus save lots of energy!)??

Efficiency of an engine with high temp of 500 C: $$(773-298)/773=.614$$

These days...

  • almost all electricity is generated using heat engines.
  • almost all transportation is powered by heat engines.

Gas engines: Fuel and gas are compressed, and then ignited with a spark plug.

When you compress a gas it gets hotter. Problem: pre-ignition, so, you'd better not go above the temperature for spontaneous ignition

Diesel engines: No spark plug. Air is compressed to a greater pressure than in a gas engine, get's way hot, then diesel is sprayed in and ignites spontaneously.

Gas in the UK currently costs ~2.5 $\times$ U.S. gasoline (> $7 / gallon)

35-50% of passenger cars sold in Europe are diesels.

 

Should you always avoid the lowest efficiency heat engines? Must the exhausted heat *always* be wasted?

Look up "co-generation"...

Possible downsides of diesel engines??

Things run down

Thermal energy has a lower "quality" in this sense:

  • All other energy forms $\rightarrow$ ThermalE: Easy to convert 100% to ThermalE.
  • ThermalE $\rightarrow$ any other energy form: Efficiency is often pretty low. Typical value in 21st century U.S.A:

    Efficiency is about 1/3=33%

If you heat your house with electricity, let's say that the electricity was generated by burning natural gas at a utility generator. What's the overall efficiency?

What's the efficiency of a natural gas furnace for your home? When you burn natural gas some of the heat escapes up the exhaust chimney and some stays in your house. The efficiency for a furnace is the ratio of the heat that stays in your house to the chemical energy released as heat during combustion. Look up "high efficiency furnace" to see what modern home furnaces on the market can do.

Which scheme above releases more carbon into the atmosphere? How much more?

What if the generating plant is burning coal instead of natural gas? Carbon emissions per Joule of ThermalE from coal are 2.5 times as much as from natural gas.

Are heat engines the only kind of engines?

DC electric motors can convert ElectricE $\to$ KineticE with an efficiency of more than 90%.

Fuel cells convert ChemicalE $\to$ ElectricE with efficiencies of 40-60%.

Heat pumps use electricity to *move* heat from one place to another. For example, "geothermal" heat pumps pull heat out of water below the ground (~50 F year round) and transport the heat into a building.

They are not converting ElectricE into ThermalE, so they are not heat engines, and are not subject to the limits of the 2nd law. The heating efficiency of a heat pump: $$\text{Efficiency}=\frac {\text{ThermalE delivered to a building}} {\text{ElectricE used by pump}} $$ This ratio is generally greater than 1 for heat pumps: up to 10/1 for geothermal and 2/1 - 4/1 for air source heat pumps.

Goshen College uses geothermal heat pumps to heat some of our buildings now.

Is the human body a heat engine?

If the human body were a heat engine, what would its efficiency be??

Take $T_{in}$ = body temperature = 98.6 F, and $T_{ex}$ = atmospheric temp = 70 F. Use Google to convert those temperatures to Kelvin (absolute) temperatures.

The efficiency of a heat engine operating between those two temperatures would be... $$\frac{T_{hot}-T_{cold}}{T_{hot}}$$

But we know its actual efficiency is closer to 25%. What do we conclude about the human body?

This means our bodies are much more amazing than internal combustion engines (as if you didn't already know...): Our muscles are converting chemical energy directly to mechanical energy, without going through a stage where the chemical energy is turned into heat.

Selected responses

As the water cools, heat escapes in the form of atoms. These atoms are very random, which goes along with entropy...?

Heat is mostly a flow of energy, not atoms: What happens is that

  1. the water atoms are initially moving very fast,
  2. they collide with air molecules that are moving (on average) slowly.
  3. At the same time, the warm atoms in the initally warm pan are bumping into the cold (slow-moving) atoms of the sidewalk that the pan was set down on.
  4. After many, many collisions, the water molecules, and the pan molecules are moving, on average, slower than they were initially. The molecules in the air and in the sidewalk are moving, on average, just a little faster.
  5. When you suck a small amount of energy out of a small system (the pan of water) its temperature will drop noticably. (Its entropy decreases.)
  6. But when you add that small amount of energy to a big system (the air and sidewalk), that energy is shared around the whole system, and the temperature change might be too small to measure. But its entropy (as well as its energy) increases.
Some of the heat from the air would go into the water.

Well, no. On average the fast water molecules are losing energy, and the colder (slower) air molecules are gaining that energy.

The atoms in the water and air combine causing disorganization.

Well, no. Here it's mainly just energy that is exchanged between the pan of water and the environment. More slowly moving water molecules are more "organized" than faster moving ones.

But this change in temperature is not the only way for atomic systems to get disorganized. It is true that if you mix orange juice and pineapple juice, the resulting mixture, where orange molecules and pineapple molecules are evenly spread out in the juice pitcher is less organized that the separate juices that you started with.

Suggested exercises

Write up and 'hand in' the bold ones.

Conceptual exercises in Chapter 7: 2, 4, 6, 9, 10, 11, 13, 16, 17, 31, 34