Thermodynamics. Two objects that are in thermal equilibrium with a third object are also in thermal equilibrium with one another.

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1 Thermodynamics hy can t you heat up your morning coffee by using the heat in the room? Theroomaroundyouhas alot ofheat. Youonly need a little heat to heat up a cup of room temperature water to near boiling? The reason has to do with thermodynamics. If youheat up one end of aniron rodin a fire, one end is hot (even red hot) and the other end is cool. ait for a minute and the heat distributes through out the iron. e would say the iron rod is in thermal equilibrium. The hotter iron atoms at the hot end collide with the slower moving iron atoms further down the rod toward the cooler end. These collision transfer energy to the cooler atoms and the bar eventually reaches thermal equilibrium i.e. the entire rod has the same temperature. A way of stating this idea idea is the 0 th Law of Thermodynamics Two objects that are in thermal equilibrium with a third object are also in thermal equilibrium with one another. The 1 st Law of Thermodynamics The first law of thermodynamics is just a statement of the law of energy conservation when heat is taken into account: Change in an object s internal (thermal) energy = Heat added to a system - (external) work done by the system or stated as a formula U = Q - If you heat up a rigid airtight container, the walls don t move so no work is done by the system. All the heat energy goes into increasing the thermal energy of the air inside.

2 As another example, if heat in the form of steam is supplied to a steamengine,someoftheheatinputtotheenginegoesintomechanic work done by the engine and some goes into increasing the thermal energy of the system. The 2 nd Law of Thermodynamics Suppose you take a hot object and place it in contact with a cooler object. ithout violating the First law of Thermodynamics, we could think of the cooler object getting colder and giving up some of its thermal energy to the hot object and making it hotter. This does not happen! Heat flows from warmer objects to colder objects but never the other way around. One statement of the Second law of Thermodynamics is: Heat never of itself flows from a cold object to a hot object. TheFirstlawofthermodynamicstellsusenergycannotbecreated or destroyed. The second law law of thermodynamics tells us how it must be transformed. Considerapileofalargenumberofcoinsall headsup. Ifyoudrop the stack of coins, some will be heads and some tails. The system of coins is initially ordered and, after dropping, is disordered. Note this is an irreversible process. I can drop the coins many times and they will not end up in an all heads pile. A high temperature system can be considered to be more disordered than a low temperature system. e can state the second law as: Natural systems tend to proceed toward a state of greater disorder.

3 Consider a jar full of perfume. In the jar initially, the perfume moleculesareallorganizedi.e. theyarealltogetherinthejar. hen you remove the top, some of the molecules evaporate and diffuse through the room. The molecules are now disordered(spread through out the room.) Naturally, they will never re-concentrate back in the jar. Entropy is a mathematical quantity which measures the disorder in a system. hen entropy increases the disorder in the system increases. Entropy is defined by: S = Q T where S is the entropy, Q is the heat added to the system and T is the temperature. In terms of entropy, the second law is: S > 0 wheresistheentropy,inwords,for a real system, the entropy always increases. You can go further and writethe entropy in terms of the possible number of states of the system,. In terms of, entropy is S = k ln where k is Boltzmann s constant and ln is the natural log of the total number of possible states of the system. Ludwig Boltzmann was an Austrian physicist who connected the ideas of entropy, disorder and thermodynamics in the late 19 th century. This equation S = k ln on the Boltzmann s tombstone in Vienna.

4 Heat Engines A heat engine is a device that changes heat energy into work. ork can be obtained only when internal thermal energy flows fromahigh temperature to a lower temperature. Only part of the heat energy can be convertedto work. Some must be exhausted to a lower temperature reservoir. Nearly all engines (steam, internal combustion, jet etc) are heat engines and must obey this principle. Hot Reservoir Heat in Engine Heat out Cold Reservoir

5 The 2 nd Law of Thermodynamics tells us heat flows naturally from hot to cold. However, heat can be made to flow from cold to hot if we do work on the system. The efficiency of a ideal heat engine is the ratio of how much (thermal) energy we put into the engine to the amount of work we get out of it. The efficiency is given by: = eff = T cold = 1 - T cold here the temperatures are in Kelvin. This was worked out by a French engineer named Carnot in the early 1800 s. For example if the hot reservoir of a steam engine is at 127 o C(400 K) and the cold reservoir at 27 o C(300 K). eff = =.25 An ideal engine operating at these temperatures can only convert 25% of the heat energy to work and must expel 75% as waste heat. Notice that this formula requires that the efficiency must be less than 1. For reasonable temperatures the efficiency is much less than 1. Also note for an ideal heat engine, that the 1 st law of thermodynamics allows us to relate the reservoirs to the heat flow. Since = + Q c, then = - Q c. If we use this in Carnot s efficiency equations: Q c = 1 - T cold = 1 - Q c = 1 - T cold Q c = T cold This is a useful way to relate the heat flows to the reservoir temperatures. Refrigerators, AC and Heat Pumps

6 Aheatenginewhichhasworkinputintoittoremoveheatfromthe lower temperature reservoir and move it to the higher temperature is called a heat pump. An air conditioner is a refrigerator what removes heat from the room (at a cooler temperature) and exhausts the heat to the outside (at a higher temperature). Hot Reservoir Q H Engine Q c Cold Reservoir e still have to conserve energy so Q H = + Q C. For a perfect (Carnot) engine (refrigerator), we still have: Q c Q H = T c T H The coefficient of performance is the ratio ofhow much heat we remove from the cold reservoir to the work we have to do. For a refrigerator this is defined as: Refig. coeff. of performance = Q c A heat pump is just a refrigerator we use in the winter to pull heat from the cooler outside to the warmer inside to warm up the room. Here we define the coefficient of performance as: HP coeff. of performance = Q H One way to think of this coefficient is the amount of heat you get out for every heat unit you put in (as work). Heat pumps work well when we are pulling heat from the outside at 15 o C and move it into a 20 o C house. The performance falls off when we try to pull o

7 Internal Combustion Engines You automobile typically uses an internal combustion engine. These engines are know as 4 cycle or 4 stroke engines. The four-cycle refers to the motion of the pistons. Each up or down is a stroke or cycle. The basic working part of an internal combustion engine is a pistons which is free to move up and down inside a cylindrical hole in the engine block. Car engines aretypically have 4, 6 or 8 pistons and cylinders. At the top of each cylinder are valves which are times to open and close to allow in the air-fuel mixture or to allow exhaust gases out. The bottom of the piston has a connecting rod which connects to the crankshaft. The turning of the crankshaft applies the power of the engine to the wheels through the transmission. The four strokes are: In the first downward stroke, the air-fuel mixture is sucked into the chamber through the open intake valve. The air and fuel can be mixed in a carburetor or air can be sucked in and fuel injected directly into the cylinder. Fuel injection is the most common method on modern cars. The intake value is closed and the piston is pushed up by the

8 A typical modern internal combustion engine is far from an ideal heat engine. Only about 20% - 30% of the chemical energy available inthefuelisconvertedtousefulwork. Mostgoestowasteheatwhich is removed by the cooling system(radiator and water pump). Some islosttofrictionwhichisreducedasmuchaspossiblewithlubricants (oil). For higher efficiency, the fuel must burn as hot as possible. This is the reason for the high compression ratio. The more the air-fuel is compressed, the hotter it will burn. The compression ratio can not be made arbitrarily large because the engine would be heavier and more difficult to engineer. Actually, this approach of increasing the compression ratio is done in a diesel engine. The compression ratio is much higher. Compression ratios for a diesel engine ranging from 14:1 to as high as 24:1. The engine works much the same except the diesel is injected at the top of the compression stroke. The hot air and high pressure ignites the diesel fuel without a spark plug. Diesel engines are more massive because of the high pressures required. In addition, they can be difficult to start. They do have higher efficiency than a gasoline internal combustion engine. For all of these reasons, they are typically used ture. Typically the air-fuel is compress by a factor of 10 (10:1 compression ratio). Thespark plug fires. Thesparkplug is fired by putting a high voltage across a small gap at the base of the spark plug. The gas-fuel mixture explodes which pushes the piston down. This is the power stroke of the engine which pushes the connecting rod and turns the crankshaft. The exhaust value is open and the piston is pushed up by the crankshaft. This pushes the exhaust gases out of the engine. At this point the process starts over.

9 in trucks instead of passenger cars. Another way to make the engine more efficient is the increase the temperature by increasing the energy stored in the fuel. This is what the octane rating is on gasoline. Higher octane burns at a higher temperature. For example premium gas (95 octane 850 o C) burns 100 o C hotter than regular gas (87 octane 750 o C) Turbochargers (and supercharges) are often used on high performance cars. The turbocharger is an air pump (compressor) which forces more air into the engine cylinder during the fuel injection stroke. It gives you more power by burning more fuel but does not really increase the efficiency of the motor. It can also lead to pinging (pre-detonation of the fuel). A turbocharger is useful if you live at high altitudes where there is less air.