HeatEngines

Lesson objectives

working fluid
piston
cylinder
PV diagram
efficiency

A heat engine converts thermal energy (heat) into other forms of energy, such as mechanical work.

Real heat engines convert heat to mechanical work by manipulating the pressure, volume, temperature and/or phase of a working fluid.

Most car engines use a piston moving in a cylinder.

The trapped volume of gas inside the cylinder is the working fluid.


When heat is added to the gas, the temperature and pressure increase.

When heat is added to the gas, the temperature and pressure increase.

The increased pressure pushes the piston down. The expanding gas does work on the surroundings.

When the gas reaches its maximum volume, the pressure is released by opening a valve.

When the gas reaches its maximum volume, the pressure is released by opening a valve.

The piston does work on the gas, compressing it back to its starting position to begin a new cycle.

During compression +W is done on the gas.

ΔV is negative

During expansion +W is done on the surroundings.

ΔV is positive

Volume

Pressure

Pressure is always on the vertical axis; volume on the horizontal axis.

Pressure and volume change constantly in a heat engine.

PV diagrams are graphs that are used to illustrate and analyze these changes.

Pressure and volume change constantly in a heat engine.

PV diagrams are graphs that are used to illustrate and analyze these changes.

On a PV diagram, area equals work.

The graph on the right represents a heat engine in which pressure and volume
change as shown.

How much heat was added?

How much work has the engine done?

How efficient is the engine at converting heat into work?

At point a: volume is minimum. From a to b heat is added and pressure rises.

At point a: volume is minimum. From a to b heat is added and pressure rises.

From b to c: gas expands, doing work. In this (unrealistic) example, pressure remains constant as the gas expands.

At point a: volume is minimum. From a to b heat is added and pressure rises.

From b to c: gas expands, doing work. In this (unrealistic) example, pressure remains constant as the gas expands.

From c to d: valve opens, reducing the pressure. Heat flows out of the engine to surroundings.

At point a: volume is minimum. From a to b heat is added and pressure rises.

From b to c: gas expands, doing work. In this (unrealistic) example, pressure remains constant as the gas expands.

From c to d: valve opens, reducing the pressure. Heat flows out of the engine to surroundings.

From d to a, the piston compresses the gas back to its starting position.

The red area is the work done by the system as it expands.

The red area is the work done by the system as it expands.

The grey area is the work done on the system to compress it.

The red area is the work done by the system as it expands.

The grey area is the work done on the system to compress it.

The area enclosed by the curve equals the positive net work done by the system in one cycle.

An equal amount of negative work is done on the system.

Work

The gas returns to its original state at the end of the cycle. That means the net energy change over a full cycle is zero!

The gas returns to its original state at the end of the cycle. That means the net energy change over a full cycle is zero!

Each cycle, heat Q is added to the system, and an equal amount of work W is done by the system.

This diagram depicts a process that goes from A to B. No heat is added.

Which of the following is true?

The energy of the gas remains constant.
The gas does work on its surroundings and loses energy.
The surroundings do work on the gas and the gas gains energy.

This diagram depicts a process that goes from A to B. No heat is added.

Which of the following is true?

The energy of the gas remains constant.
The gas does work on its surroundings and loses energy.
The surroundings do work on the gas and the gas gains energy.

Why?

The gas loses energy.

Since no heat is added, energy must decrease:

From A to B the gas expands: positive work is done on the surroundings so negative work is done on the gas.

Which part of the process compresses the gas. How do you know?



Does the complete cycle absorb or give off heat? How do you know?

For this PV diagram shown:

Which part of the process compresses the gas. How do you know?



Does the complete cycle absorb or give off heat? How do you know?

For this PV diagram shown:

Compression reduces volume. This happens in process C.

Which part of the process compresses the gas. How do you know?



Does the complete cycle absorb or give off heat? How do you know?

Compression reduces volume. This happens in process C.

For this PV diagram shown:

ΔE = 0 in a complete cycle. Since the system does positive work equal to the enclosed area, Q must have been absorbed.

You might think that it is possible to invent an engine that is 100% efficient.







It turns out that this is impossible.

Assume that 100 moles of an ideal gas is taken through the cycle depicted in this PV diagram.





To find the efficiency of the engine, you must calculate work output of the engine, and the heat input.

Pressure
(atm)

1

3

1

4

Volume
(m3)

First, use the ideal gas law to find the
temperature at each part of the cycle:

where:
n = # moles of gas = 100
R = 8.31 J/mol-K

Temperature of gas:

n = 100 moles
R = 8.314 J/mol-K

Fill in the first column on your assignment sheet:

Pressure
(atm)

1

3

1

4

Volume
(m3)

Temperature of gas:

n = 100 moles
R = 8.314 J/mol-K

Check your answers:

Pressure
(atm)

1

3

1

4

Volume
(m3)

Next, calculate the internal energy of the gas, U.

U equals the average kinetic energy of each molecule multiplied by the number of molecules, N:

This can be rewritten in terms of moles, n:

Internal energy:

n = 100 moles
R = 8.314 J/mol-K

Calculate internal energy (U) at each point:

Pressure
(atm)

1

3

1

4

Volume
(m3)

Internal energy:

n = 100 moles
R = 8.314 J/mol-K

Check your answers:

Pressure
(atm)

1

3

1

4

Volume
(m3)

Pressure
(atm)

1

3

1

4

Volume
(m3)

Use the energies from Table 1 to find the change in energy ΔE for each part of the cycle.

Check your answers:

Pressure
(atm)

1

3

1

4

Volume
(m3)

Use the energies from Table 1 to find the change in energy ΔE for each part of the cycle.

Pressure
(atm)

1

3

1

4

Volume
(m3)

Calculate the work done ON the gas in each part of the cycle. (1 atm ≈ 100,000 Pa)

Pressure
(atm)

1

3

1

4

Volume
(m3)

Check your answers:

Calculate the work done ON the gas in each part of the cycle. (1 atm ≈ 100,000 Pa)

Pressure
(atm)

1

3

1

4

Volume
(m3)

Pressure
(atm)

1

3

1

4

Volume
(m3)

Check your answers:

Pressure
(atm)

1

3

1

4

Volume
(m3)

Calculate the efficiency on your answer sheet:

Pressure
(atm)

1

3

1

4

Volume
(m3)

Check your answer:

This thermodynamic cycle has a miserable efficiency of 25%.

Heat not converted to work is rejected to the surroundings in segments c to d and d to a.

No heat engine can convert 100% of heat input to work output.

There are no perfect engines.

This is a consequence of the second law of thermodynamics – the law of entropy.

The work done is always LESS than the heat added.

During each cycle, an engine receives 690 J of heat from a hot reservoir, and gives off 430 J of heat to a cold reservoir. What is:

the work done on the surroundings?


the efficiency of this engine?

During each cycle, an engine receives 690 J of heat from a hot reservoir, and gives off 430 J of heat to a cold reservoir. What is:

the work done on the surroundings?





the efficiency of this engine?

the work done on the surroundings?





the efficiency of this engine?

During each cycle, an engine receives 690 J of heat from a hot reservoir, and gives off 430 J of heat to a cold reservoir. What is: