## Heat Engines

#### Introduction

The generic definition of a heat engine is any device which takes heat for its input and turns part of it into work. That part of the heat energy which is not turned into work is returned to the environment as waste heat. Practical devices include some obvious ones, as well as some not so obvious ones
• Stem engine
• Gasoline engine
• Diesel engine
• Power station, in which a fuel is used to heat water, which in turn drives a turbine to generate electricity
• A hurricane, whiich uses the thermal energy of warm tropical waters to develop from a small disorganized low pressure system into a raging destructive storm

#### The gasoline engine as a heat engine

The gasoline engine is a four stroke engine which burns a mixture of gasoline and air to produce very hot gas in any one of a set cylinders (usually either 4, 6, or 8) and uses the expansion of the very hot gas to produce useful work. At the end of the process the hot gas is exhausted to the atmosphere. The term 'four stroke' refers to the four different parts which make up the one cycle of the engine
1. The piston is drawn down, drawing in a fuel/air mixture through an entry valve.
2. The entry valve closes, and the piston is drawn back up, compressing the fuel/air mixture
3. A spark ignites the fuel/air mixture. The production of heat caused by the burning of the fuel is the heat input to the engine. As a result of the explosive burning of the gas the piston is forced down, creating the work that the engine produces.
4. Finally the exit valve opens, and the piston rises again, forcing the spent fuel out of the cylinder. The gas is still quite hot, and so carries the waste heat away from the engine.
After the completion of the full cycle the engine returns to original state, ready to repeat the cycle again. The temperature has not changed, and so there is no change in the internal energy of the engine. There has been heat put into the engine (Q1) and some heat taken out again (Q2). We can then write from the First Law of Thermodynamics

 Q1 - Q2 = W

#### Efficiency of a heat engine

Efficiency is defined as the ratio of the work that is extracted from the engine to the heat energy that has to be put in

 Efficiency = W Q1
Using the equation above from the First Law of Thermodynamics we can write this as

 Efficiency = W = Q1 - Q2 = 1 - Q2 Q1 Q1 Q1

Suppose that an engine is built which for each four stroke cycle 25 MJ of heat (Q1) produces 8 MJ of work.

• The amount for heat exhausted to the atmosphere would be Q2 = Q1 - W = 25 MJ - 8 MJ = 17 MJ
• The efficiency would then be W/Q1 = 8/25 = 0.32 (32 %)

#### The Carnot Engine

The Carnot Engine is not a real engine. It is a mathematical model, the limit representing the best possible efficiency that a heat engine could possibly have. Although it can never be built it is useful in giving us an upper limit to the best engine that we can hope to build.
Its efficiency is determined by the Second Law of Thermodynamics, and depends on only two temperatures, the temperature of the hot gas (TH) and the temperature of the atmosphere where the exhaust gases go (TC). The efficiency is equal to

 Efficiencyc = 1 - TC TH

Suppose that our Carnot engines operates between the two temperatures = 900 oC = 1173 K and 50 oC = 323 K. The efficiency of the Carnot engine would be

 Efficiencyc = 1 - 323/1173 = 1 - 0.275 = 0.725 (72.5 %).

A real engine using these two temperatures must have an efficiency less that this (often much less).