Heat Engines A Brief Review of Thermodynamics

Thermodynamics  The science of thermodynamics deals with the relationship between heat and work.  It is governed by two laws, neither of which have ever been proved.  On the other hand no violations of either law have ever been observed.

First Law of Thermodynamics  The energy that can be extracted from a process can never be more than the energy put into the process  In other words  Energy out = Energy in  This is essentially the law of conservation of energy, i.e.  Energy can be neither created nor destroyed, it can only be converted from one form to another

The second law of thermodynamics  The first law is concerned with the totality of energy in a process  The second law tells us how much work we can extract from a given amount of heat.  Carnot’s statement was to the effect that we cannot convert all the the available heat into work.  The second law is also concerned with whether a process can occur at all. For example,  Heat will always flow from a high to a low temperature  A gas under pressure will expand; compression does not occur naturally

Heat Engines  A heat engine is a device for extracting work from a hot fluid. For example  A car engine extracts power from the combustion of fuel with air  A steam steam turbine extracts power from steam  Both of these function by allowing a hot fluid to expand so as to cause motion in a critical component of the engine.  In the process, high grade energy is said to be degraded to lower grade energy.

An ideal heat engine  The diagram on the right represents an ideal heat engine  Heat is added at constant temperature to the fluid at the high temperature source  The fluid flows through an expansion device where work is done, and the temperature of the fluid falls from T H to T L  Heat is then rejected at constant temperature at the low temperature source.

Closed Cycle Heat Engine  The cycle in the previous slide is known as an open cycle.  The closed cycle here has four stages  Isothermal heat addition  Adiabatic expansion  Isothermal heat removal  Adiabatic compression  Isothermal = const. Temp  Adiabatic = perfectly insulated

The Carnot Engine  The cycles above are examples of the Carnot engine.  In the Carnot cycle all processes are reversible.  In a Carnot engine, the maximum work that can be done, and hence the efficiency of the ideal engine depends on the temperatures T H and T L  The efficiency of a Carnot engine is given by  The temperature is in the Kelvin or absolute scale  This efficiency is called the Carnot efficiency

Practical heat engines (1)  The Carnot engine represents the theoretical limit and is not a practical engine.  The main limitations of the Carnot engine are:  The processes in all four stages are reversible. For this to be the case they must all take place infinitely slowly  The work extracted on expansion is equal to the work required for compression, so no net work is extracted.  A practical heat engine has a lower efficiency than a Carnot engine, but can make more effective use of the energy in the hot fluid.

Practical Heat Engines (2)  Practical Heat Engines include:  The Rankine cycle – basis of steam engines in power stations  Otto and Diesel cycles – internal combustion engines  Gas turbine  These have lower efficiencies than the Carnot cycle but are permit useful work to be extracted.

The Rankine cycle  This has two differences to the Carnot cycle  There must be reasonable temperature differences in the boiler and condenser to ensure that heat addition and rejection occurs at an acceptable rate  The turbine exhaust is completely condensed and returned to the boiler by a pump. This uses very much less energy than a compressor.  These result in lower efficiencies than the Carnot cycle but permit useful work to be done.

Other cycles  Otto, Diesel and Gas turbines all involve an initial compression stage, but are otherwise open cycle processes.  Combined cycle gas turbine:  This combines a gas turbine with a Rankine steam cycle to maximise the work extracted from the fuel.  Efficiencies are much closer to Carnot efficiencies than in other practical cycle used to date.

Example  Steam from a geothermal well is expanded in a Carnot engine from a temperature of 150  C to 50  C. How much work is extracted from 1kg of steam?  If the steam is heated to 250  C before expansion, how much work is now extracted in relation to the extra heat added  Heat capacity of steam = 1.9 kJ kg -1 K -1  0  C = 273 K

Solution Energy extracted = 1  1.9  100 = 190 kJ Efficiency After heating to 250: Energy extracted = 380 kJ Efficiency = 38%

And Finally... Work is heat and heat is work and all the heat in the universe is gonna coooool down! Yeh! That’s entropy man. Michael Flanders and Donald Swann