Thermal Reservoirs and Heat Engines A conceptual schematic of a heat engine. Two channels of heat transfer, with thermal reservoirs of two different temperatures TH and TL, are shown, along with one channel of work transfer.. (URL for notes: http://www.colorado.edu/ASEN/asen3113)
• The thermal reservoirs are assumed to be large enough that their temperatures don’t change as heat flows in or out of them. • The arrows indicate the direction of energy transfer (heat flow or work) in the forward time direction. • According to the first law of thermodynamics we have Q = W + q. • The efficiency h of this engine is defined as the ratio of work energy output to the heat energy input, so we have h = W/Q = 1 – q/Q
All heat engines: Receive heat from a high-temperature source (solar energy, blast furnace, ocean, land surface, etc.) Convert part of this heat to work Reject the remaining waste heat to a low-temperature sink (the atmosphere, rivers, etc.) Operate on a cycle Have a working fluid
Qin boiler Compress to boiler pressure turbine pump Wout condenser Qout Wnet = Wout - Win = Qin - Qout Heat Engine Components
• The Rankine cycle is a thermodynamic cycle. • Like other thermodynamic cycles, the maximum efficiency of the Rankine cycle is given by calculating the maximum efficiency of the Carnot cycle. • It is named after William John Macquorn Rankine, a Scottish scientist.
• Rankine cycles describe the operation of steam heat engines commonly found in power generation plants. • In such power plants, power is generated by alternately vaporizing and condensing a working fluid (in many cases water, although refrigerants such as ammonia may also be used).
• The working fluid in a Rankine cycle follows a closed loop and is re-used constantly. • Water vapor seen billowing from power plants is evaporating cooling water, not working fluid. (NB: steam is invisible until it comes in contact with cool, saturated air, at which point it condenses and forms the white billowy clouds seen leaving cooling towers).
Understanding Thermal Reservoirs Bodies that don’t change their temperature even though heat is being added or subtracted. Blast furnce; hot enough that heat removed does not change the temperature of the furnace. Large lake or ocean; large enough that temperature changes only very slowly in spite of heat entering or leaving at the surface. Land beneath the surface; temperature remains constant even though heat energy is transferred from the surface.
The Underground Motels and Church in Coober Pedy, Australia outside 90-120 °F, inside constant 70 °F
Thermal Efficiency Basic Heat Engine LTER= Low Temperature Energy Reservoir HTER= High Temperature Energy Reservoir The thermal efficiency of a cycle (or more precisely a forward heat engine) is defined as the ratio of net work output, W, to the heat supplied at high temperature, Q1, i.e. or net work/total heat in
Calculate the maximum theoretical thermal efficiency of a coal-fired power station that heats steam to 510°C and cools it in a condenser at 30°C. • Answer: Maximum efficiency = (THOT – TCOLD)/THOT • = [(510+273) – (30+273)] / (510+273) • = 480 / 783 = 0.61 or 61%
2. The temperature of the gases in a car engine during combustion is 1800°C. The exhaust is expelled at 80°C. Calculate the maximum theoretical thermal efficiency of the engine. Answer: Maximum theoretical efficiency = (THOT – TCOLD)/THOT = [(1800+273) – (80+273)] / (1800+273) = 1720/2073 = 0.83 or 83% Of course, in both case, the actual efficiency will be smaller. Students should consider why.
Second Law of Thermodynamics: Kelvin-Planck Statement It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work. Thus, a heat engine must exchange heat with a low temperature sink as well as a high temperature source to keep operating.
or No heat engine can have a thermal efficiency of 100%, or for a power plant to operate, the working fluid must exchange heat with the environment as well as the furnce (must have waste heat).
If all the energy transfer processes in a given heat engine are reversible, we can just as well reverse all the arrows, and run the heat engine “backwards in time”. (A kitchen refrigerator is a common example of a heat engine running in reverse.)
Second Law of Thermodynamics The maximum efficiency which can be achieved is the Carnot efficiency.
The Diesel Engine The diesel internal combustion engine differs from the gasoline powered Otto Cycle by using a higher compression of the fuel to ignite the fuel rather than using a spark plug ("compression ignition" rather than "spark ignition").
Processing crude oil - refining Some properties of crude oil fractions. How bubble caps work
In the diesel engine, air is compressed adiabatically with a compression ratio typically between 15 and 20. This compression raises the temperature to the ignition temperature of the fuel mixture which is formed by injecting fuel once the air is compressed.
Diesel Engine Theoretical Efficiency Since the compression and power strokes of this idealized cycle are adiabatic, the efficiency can be calculated from the constant pressure and constant volume processes. The input and output energies and the efficiency can be calculated from the temperatures and specific heats:
It is convenient to express this efficiency in terms of the compression ratio rC = V1/V2 and the expansion ratio rE = V1/V3. The efficiency can be written and this can be rearranged to the form Theoretical Diesel Efficiency (what does we assume?)
Nuclear power plant; thermal rods in water Simulation of temperatures inside a nuclear reactor. From Argonne
A nuclear power station. The nuclear reactors are inside the two cylindrical containment buildings in the foreground—behind are the cooling towers (venting water vapor). Steam from cooling towers
U.S. commercial pressurized water reactor (PWR) nuclear power plants Nuclear power generator
The picture above shows the release of steam from geothermal plants in Santa Rosa -- geothermal plants tap the heat within the Earth to produce energy in the form of electricity.The heat trapped within the Earth, which was generated during its formation billions of years ago and through the decay of radioactive elements with rocks, is trying to escape Earth as a heat engine
Convection, also occurs within the Earth as hot, less dense portions of the mantle rise and displace cooler, denser rocks, which then sink into the mantle -- in summary the cooler, dense rocks sink in the mantle, whereas the warmer rocks within the mantle rise by a process called mantle convection (shown by red arrows in the diagram above).
Andes Mountains in South America, which in this particular locale are composed of sediments that formed on the seafloor -- miles below the sea surface -- millions of years ago. Now these sediments rest on the top of the mountains, miles above the sea surface -- how can this be? How can something as heavy as the surface of the Earth rise to such a high elevation? Mountains of molten rock, or lava, on the big island of Hawaii. Once again, how can molten (liquid) rock at temperatures more than 1000oC find its way to the surface of the Earth and why should this happen in Hawaii?
Here is a map of the major plates that make up the surface of the Earth.These plates are formed by a strong, rigid surface layer of rocks between 80 and 300 kilometers-thick.
• Harry Hess was the first to come up with an explanation for the mid-ocean ridges -- he suggested that the seafloor was created by volcanism within the rift valley along the axis of the ridge. • With time the seafloor and underlying crust will spread away from the ridge in opposite directions on either side -- thereby creating a mobile seafloor -- like a conveyor belt -- very interesting idea, which he called seafloor spreading.
• How do we know that the seafloor is spreading at the mid-Atlantic ridge? • Reversals in the polarityof magnetic materials in the seafloor that formed at geologic periods when the Earth’s magnetic field was reversed. • What does that mean for us on Earth if the magnetic field reverses?
• The time-scale of the magnetic field reversals is shown at the top. • Regions with orange or yellow patterns denote time of "normal polarity" or a magnetic direction with the same direction as today's field. • The white regions represent times when the field was in the opposite (or reversed) direction from what it is today.
Here you see a map of the mid-ocean ridge system. The ridge in the Pacific is called the East Pacific Rise, in the Atlantic is is called the Mid-Atlantic Ridge, and in the Indian Ocean it is either the Southwest Indian Ridge, Central Indian Ridge or Southeast Indian Ridge.
Formation of Hurricane A Giant Heat Engine Waves in the trade winds in the Atlantic Ocean—areas of converging winds that move along the same track as the prevailing wind—create instabilities in the atmosphere that may lead to the formation of hurricanes. Hurricanes form when the energy released by the condensation of moisture in rising air causes a chain reaction. The air heats up, rising further, which leads to more condensation. The air flowing out of the top of this “chimney” drops towards the ground, forming powerful winds
Hurricane or tropical cyclone/typhoon Hurricane Katrina on August 28 at 1:00 pm EDT Schematic representation of flow around a low-pressure area in the Northern hemisphere. The pressure gradient force is represented by blue arrows, the Coriolis acceleration (always perpendicular to the velocity) by red arrows Why do these two storms rotate in opposite directions? Image of Cyclone Catarina on March 26, 2004, the first South Atlantic hurricane ever recorded
Sadie Carnot • French engineer 1796 - 1832 (Paris) • Father was involved in the French revolution and was exciled • Sadie Carnot joined the military and became interested in steam engines. • He worked with his brother on steam engines and did experiments similar to those of Joule 20 years before Joule. • He died of Cholera at the age of 36.
Carnot Cycle • The most efficient heat engine cycle is the Carnot cycle, consisting of twoisothermal processes and two adiabatic processes. The Carnot cycle can be thought of as the most efficient heat engine cycle allowed by physical laws. • When the second law of thermodynamics states that not all the supplied heat in a heat engine can be used to do work, the Carnot efficiency sets the limiting value on the fraction of the heat which can be so used. • In order to approach the Carnot efficiency, the processes involved in the heat engine cycle must be reversible and involve no change in entropy. • This means that the Carnot cycle is an idealization, since no real engine processes are reversible and all real physical processes involve some increase in entropy.
Engine Cycles • For a constant mass of gas, the operation of a heat engine is a repeating cycle and its PV diagram will be a closed figure. • The idea of an engine cycle is illustrated below for one of the simplest kinds of cycles. • If the cycle is operated clockwise on the diagram, the engine uses heat to do net work. • If operated counterclockwise, it uses work to transport heat and is therefore acting as a refrigerator or a heat pump.