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CLASSNOTES II: Ch.14&15. Thermodynamics - concerned with relationships between heat and other forms of energy (mechanical, light, sound, chemical, electromagnetic, nuclear, atomic). Zeroth Law: Temperature is the indicator of thermal equilibrium. First Law: Energy is conserved.
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CLASSNOTES II: Ch.14&15. • Thermodynamics - concerned with relationships between heat and other forms of energy (mechanical, light, sound, chemical, electromagnetic, nuclear, atomic). • Zeroth Law: Temperature is the indicator of thermal equilibrium. • First Law: Energy is conserved. • Second Law: Disorder (entropy) tends to increase.
First Law Equation:ΔU = (Uf -Ui) = Q-W Types of Thermal Processes) A thermal process is considered quasi-static when it occurs slowly enough that a uniform pressure and temperature exist throughout the system at all times. ProcessOccurs at or with Isobaric - constant pressure. Isochoric - constant volume. Isothermal - constant temperature. Adiabatic - takes place without the transfer of heat.
Work Done By a Gas: W = P·ΔV , Pressure x change in Volume. Moving boundary GAS 2 kg 3 m3 GAS 2 kg 1 m3 Fixed boundary
Carnot Efficiency Most efficient way of running a heat engine. Sadi Carnot (1796-1832) Paris, come up with the cycle. In his paper, “Reflections on the Motive Power of Heat”, we find, for a Carnot efficiency: Efficiency = (Thot - Tcold) / Thot = 1 – (Tcold / Thot) . Temperatures must be (Kelvin), not oC or oF . Due to material limitations on both Thot and Tcold, this efficiency is about 30%.
Laws of Thermodynamics - First Law Equivalence of different forms of energy ΔU = Q - W - Second Law Only fraction of thermal energy can be used to do mechanical work Eff = 1 – (Tcold / Thot) - Zeroth Law Temperature is ONLY measure of thermodynamic equilibrium
Heat Engines Our heat engines, whether fired by coal, oil or nuclear energy, are all limited in their Carnot efficiency. Efficiency = 1 – (Tcold / Thot) . Note that for the best efficiencies, we need Thot to be very hot and Tcold to be very cold. Due to material limitations on both Thot and Tcold, this efficiency is about 30%.
HISTORY OF HEAT ENGINES: • Hero’s Engine: • 100 BC, a Greek inventor, Hero of Alexandria. • Depended on the mechanical interaction of heat and water.
2. Thomas Savery (1650-1715)English military engineer and inventor who in 1698, patented the first crude steam engine, based on a pressure cooker invented in 1679.
3. Thomas Newcomen (1663-1729) A British blacksmith, who invented the atmospheric steam engine, an improvement over Thomas Savery's previous design.
In the 1800’s, US, Fulton and Watt perfected the steam engine. Eff increased from 2% to 20% • Reasons: 1. Larger engines, 2. Higher pressure and temperature, 3. Special alloys • Steam engine replaced by steam turbine and gasoline engine. • 2 types of heat engines: 1. Internal combustion, 2. External combustion.
Number of moles n in a sample equals the number of particles N (atoms or molecules) in the sample divided by the number of particles per mole NA. Or n = N/NA where NA = 6.022x1023 particles per mole (Avogadro’s Number) Amedeo Avogadro (1776-1856), Turin, Italy. Number of moles also equals mass m of the sample (in grams) divided by the mass per mole (in grams per mole ). n = m/(mass per mole). Mass of a particle (in grams) can also be obtained by dividing mass per mole (in g/mol) by Avogadro's number. mparticle = mass per mole/NA.
Temperature is a quantity proportional to the average kinetic energy of the particles. KEavg = ½ mv2rms where vrms is the root-mean-square speed of the particles, derived statistically by Boltzmann. The internal energy U of n moles of a monatomic ideal gas is U = 3/2 nRT. Ludwig Boltzmann (1844-1906), Austria, who developed the branch of Physics known as Statistical Mechanics.
Fick’s Law, named after Adolf Eugen Fick (1829-1901), Germany. The mass of a solute that diffuses in time through a channel of known length, L, and cross-sectional area, A, is given by m = (D·A·ΔC)t/L . ΔC is the solute concentration difference between the ends of the channel D is the diffusion constant.
Zeroth Law of Thermodynamics: “Two systems are in thermal equilibrium if there is no net heat flow between them when they are brought into thermal contact.” First Law of Thermodynamics: “The total increase in thermal energy of a system is equal to the sum of the heat added to it and the work done on it.” ΔU = (Uf -Ui) = Q-W The second law also states that natural processes always go in a direction that increases the entropy, S, unavailable energy, or disorder, of a system. ΔS = Q – W. A thermal process is considered quasi-static when it occurs slowly enough that a uniform pressure and temperature exist throughout the system at all times.
The work done in any kind of quasi-static process is given by the area under the pressure versus volume graph. W = nRT·ln(Vf /Vi). 1. An isobaric process is one that occurs at constant pressure. W = P·ΔV = P(Vf -Vi). 2. An isochoric process is done at constant volume and no work is done. W = 0 3. An isothermal process is done at constant temperature. W = 0 4. An adiabatic process takes place without the transfer of heat. W = 3/2 nR(Ti -Tf)
For an Adiabatic Process, ideal gas obeys: 1. Ideal Gas Law, PV = NRT 2. PiViγ = PfVfγ, where γ = cp/cv, ratio of specific heat capacities at constant pressure and constant volume. The molar specific heat capacity of a substance determines how much heat is added or removed when the temperature of n moles of the substance changes. This is given by the equation Q = C·n·ΔT. For a monatomic ideal gas, the molar specific heat capacities at constant pressure and constant volume are, respectively, CP = 5/2 R and CV = 3/2 R, where R = 8.31 J/(mol·K) the Ideal Gas Constant. For any ideal gas, the difference between CP and CV is R, or CP - CV = R.
A heat engine continuously converts thermal energy to mechanical energy and does work. The efficiency, e, of a heat engine is expressed by the equation e = (Work done)/(Input heat) = W/QH. Conservation of energy requires that QH = W + QC . Combining the equations we get, e = 1 – (QC / QH ). From Carnot, we have QC/QH = TC/TH. This gives an equation for the maximum efficiency that an engine can have operating between two fixed temperatures. e Carnot = 1 - TC/TH.
A heat pump, air conditioner, or refrigerator uses mechanical energy to transfer heat from an area of lower to higher temperature. These are governed by the Law of Conservation of Energy with QH = W + QC. The coefficient of performance of a refrigerator or air conditioner is given by the equation Coefficient of performance = QC /W. For the heat pump which also moves heat from a cold area, we have a similar relationship, Coefficient of performance = QH/W.
Famous Early Automobile Makers 1. Nicolaus August Otto invented the gas motor engine in 1876. 2. In 1885, Gottlieb Daimler invented a gas engine that allowed for a revolution in car design. 3. Karl Benz was the German mechanical engineer who designed and in 1885 built the world's first practical automobile to be powered by an internal-combustion engine. Named it Mercedes, after his daughter.
1900’s: Jet engines were developed. • Rely on Newton’s 3rd Law (action/reaction) to produce motion. • RamJet - simple, no moving parts, must be moving to operate, propelled by a rocket. • Supersonic? Scramjet.
2. TurboJet- turbine (fan blades) used to force air into combustion chamber. Thrust produced by escaping hot gases. Auxiliary power must start engine. Ex. Today’s jet engines.
3. Rocket – reaction force (thrust) produces motion. Carries fuel and oxygen needed for combustion. Travels beyond atmosphere. Specific Impulse of the fuel, S.I. = (Thrust / Weight) x Time SPECIFIC IMPULSE
4. DIESEL ENGINE –developed by Rudolf Diesel (1858-1913), Germany. Fuel is compressed to ignition temperature. Low power to weight ratio. Cheaper fuel (at one time).
5. Gas turbine – continuously drawn-in air. Fan blades. Fuel burns with steady flame. Gasses pass through exhaust nozzle at high speed. Runs its own turbine. Used in aircraft.
Efficiencies of Power Plants The End. Or is it? Power plants these days (almost all of which are heat-engines) typically get no better than 33% overall efficiency.
