The Carnot Cycle

MEE1018: Thermodynamics - Lecture 10

Reversible process

One which after having taken place can be reversed back to its initial conditions without any changes having occurred to the system or surroundings.

Reversible process in a cylinder

If work is done compressing a cylinder and can then extract all the work and return the system and surroundings to its original state, the process is reversible.

Importance of reversibility process

• They were easy to analyse

• They served as idealised models

• They give theoretical limits

Irreversible processes

Any processes that cannot be reverse in this way (real processes).

Factors that cause a process to be irreversible

• Friction and air resistance - friction turns work into heat, an irreversible process

• Unrestrained expansion - irreversible as they turn work into heat

• Heat transfer across a finite temperature difference - second law as well

• Mixing of two fluids

• Electrical resistance

• Chemical reactions

• Inelastic deformation of solids

Carnot Engine

The heat engine that operates on the most efficient cycle between high and low temperature reservoirs.

Carnot cycle

The ideal engine that uses reversible processes to form its cycle.

Very useful as it establishes the maximum possible efficiency of any real engine.

If the efficiency of a real engine is significantly below that of the ideal Carnot engine operating under the same conditions,

Then it demonstrates that improvements may be made.

The Carnot Cycle p-v diagram

1-2 Reversible isothermal expansion - Heat is transferred from the high temperature sink e.g. a furnace, passes to the working fluid (e.g. in a boiler).

2-3 Reversible adiabatic expansion - Working fluid is expanded through a turbine, work is produced.

3-4 Reversible isothermal compression - Heat is transferred to the low temperature sink

4-1 Reversible adiabatic compression - Working fluid is compressed e.g. in a pump. Work is input.

Efficiency of the Carnot Engine

Applies to all reversible heat engines and gives us the maximum theoretical possible efficiency that could be obtained by an engine working between those two temperatures.

Where Q_L is the heat rejected from heat engine to sink, Q_H is the heat flow from source of heat engine, T_L is the temperature of sink and T_H is the temperature of sink.

Carnot Principles

1. The efficiency of an irreversible heat engine is always less than the efficiency of a reversible one operating between the same two reservoirs.

2. The efficiencies of all reversible heat engines operating between the same two temperatures are the same.

Coefficient of performance for a refrigerator

Coefficient of performance for a heat pump

Entropy (S)

The effect where energy wants to “spread out” from being localised in one place.

A measure of disorder.

A property of a system.

Entropy unit

J/K

Specific entropy (s) - J/kg.K

Natural tendency of entropy

To always increase. Everything we do increases the entropy of the universe.

Maximum entropy

There will come a point where all energy is “evenly spread”, i.e. there is thermodynamic equilibrium. This is the point of maximum entropy.

At this point, there will be no driving force for processes to occur, a theory known as the heat death of the universe.

Isentropic process

A process during which the entropy remains constant.

Adiabatic and reversible.

Δs = 0

Adiabatic process

PV^k = C

T-S diagram of Carnot Cycle

1-2 Isothermal expansion with heat transferred from the high temperature reservoir.

2-3 Adiabatic reversible expansion an isentropic process

3-4 Isothermal compression, with heat transferred to the low temperature reservoir.

4-1 Adiabatic reversible compression back to original conditions an isentropic process

Reasons why the Carnot Cycle is impractical

1. Limited max temperature.

2. Reversible isothermal processes very difficult to achieve.

3. Process 4-1 requires pumping of a liquid/vapour mixture (which is hard to achieve).

4. During 2-3 the liquid/vapour mixture needs to be expanded through a turbine. The water droplets cause erosion of the turbine blades. (Superheated stream would not cause this issue).

5. It is difficult to achieve just the right amount of heat rejection between 3 and 4.

6. Despite the high efficiency, actual work output is low.

Poor work output of Carnot Cycle

The work done in a cycle is equal to the area enclosed in the T-S diagram.

For a steam Carnot cycle, the maximum temperature that it can operator at is 374°C.

As we approach this temperature, the work output decreases as you can see from graph.

Analysis of Power Cycle

Assume positive values in all cases. Simply take the larger enthalpy value in each case and subtract the smaller value.