Thermodynamics Temperature Heat Work Heat Engines Thermodynamics n

Thermodynamics Temperature, Heat, Work Heat Engines

Thermodynamics n n In thermodynamics we deal with the energy and work of a system. We describe the system in terms of observables which are the net result of the mechanics quantities of all the molecules which make up the system.

Thermodynamics n These observables are Volume n Temperature n Pressure n Heat energy n Work n n Thermodynamics deals with those quantities and their relationships.

We all know about Volume. n Pressure: n

Example n n n 120 lb person putting all their weight on 2 in 2 of heels. Pressure = 120 lb/2 in 2 = 60 lb/in 2. Is that a lot? Comparison: 1 atm = 14. 7 lb/in 2. Thus of heels is approximately 4 atm. This is the pressure you would feel at a depth of approximately 135 ft of water.

Temperature and Heat n n n Everyone has a qualitative understanding of temperature, but it is not very exact. Question: Why can you put your hand in a 400 F oven and not get instantly burned, but if you touch the metal rack, you do? Answer: Even though the air and the rack are at the same temperature, they have very different energy contents.

Temperature and Heat n n Temperature is a measure (indicator) of the amount of heat energy in a system Temperature is a measure (indicator) of the average kinetic energy of the molecules in a system

Construction of a Temperature Scale Choose fixed point temperatures that are easy to reconstruct in any lab, e. g. freezing point of water, boiling point of water, or anything else you can think of. n Fahrenheit: Original idea: 0 F Freezing point of salt/water mix 100 F Body Temperature Using this ice melts at 32 F and water boils at 212 F Note: 180 F between boiling an freezing. n

Celsius (Centigrade) Scale: 0 C Ice Melts 100 C Water Boils Note a change of 1 C = a change of 1. 8 F. n

Conversion between Fahrenheit and Celsius

Absolute or Kelvin Scale n n The lowest temperature on the Celsius Scale is -273. 15 C. Based on gas pressure going to zero

Absolute or Kelvin Scale

Absolute or Kelvin Scale n n The lowest possible temperature on the Celsius Scale is -273. 15 C. The Kelvin Scale just takes this value and calls it 0 Kelvins, or absolute zero. Note: the size of 1 K is the same as 1 C. To convert from C to K just add 273. 15 K = C + 273. 15

When do you use which scale. n n n Fahrenheit: everyday use (the weather). Use either Kelvin or Celsius when measuring differences in temperature. Use Kelvin when doing absolute temperature measurements or calculating energies or pressures

Temperature Conversions § F = 9/5 C + 32 § C = 5/9(F - 32) § K = C + 273. 15

Temperature Conversions § F Why the “ 32” between Fahrenheit and Celsius?

Why the “ 32” between Fahrenheit & Celsius? A. B. C. Different-sized units Different zero points Different temperature references

Temperature Conversions n Convert 50º F to Celsius

Convert 50º F to Celsius A. B. C. D. 32º C 28º C 10º C

Temperature Conversions n Convert 50º F to Celsius C = 5/9(F - 32) C = 5/9(50 - 32) = 10º C n Convert 10º C to Kelvin n n

Temperature Conversions n Convert 50º F to Absolute

Convert 50º F to Absolute A. B. C. D. 283. 15 K -273. 15 K 50 K 10 K

n n n Temperature is a measure of the average kinetic energy of the molecules in a body. The higher the temperature, the faster the particles (atoms/molecules) are moving, i. e. more kinetic energy. We will take heat to mean thermal energy in a body OR thermal energy transferred into/out of a body

Specific Heat n n Observation: It is easy to change the temperature of some things (e. g. air) and hard to change the temperature of others (e. g. water) Specific heat c describes how much energy Q is needed to change the temperature ( T) of an body of mass m c is the specific heat and is a property of the material. Note: since we are looking at changes in temperature, either Kelvin or Celsius will do.

Units of Heat n n n Heat is a form of energy so we can always use Joules. More common in thermodynamics is the calorie: By definition 1 calorie is the amount of heat required to change the temperature of 1 gram of water 1 Cal = 1 food calorie = 1000 cal.

n n The English unit of heat is the Btu (British Thermal Unit. ) It is the amount of heat required to change the temperature of 1 lb of water 1 F. Conversions: 1 cal =4. 186 J 1 Btu = 252 cal

Water has a specific heat of 1 cal/g. K and iron has a specific heat of 0. 107 cal/g. K. If we add the same amount of heat to equal masses of iron and water, which will have the larger change in temperature? 1. 2. 3. 4. The iron. They will have equal changes since the same amount of heat is added to each. The Water. None of the above.

Example Calculation n Compare the amount of heat energy required to raise the temperature of 1 kg of water and 1 kg of iron 20 C?

Heat Transfer Mechanisms 1. 2. 3. Conduction: (solids--mostly) Heat transfer without mass transfer. Convection: (liquids/gas) Heat transfer with mass transfer. Radiation: Takes place even in a vacuum.

Conduction

Example

Convection Examples n Ocean Currents

n Plate tectonics

Radiation Everything that has a temperature radiates energy. n Method that energy from sun reaches the earth. n

Radiation Energy Transfer Wein’s Displacement Law n lp. T = 2. 898 x 10 -3 m∙K n Stefan-Boltzmann Law n I = s. T 4 W/m 2 n P = Q/t = se. AT 4 W n s = 5. 670 x 10 -8 W/m 2 K 4 n

Radiation Everything that has a temperature radiates energy. n Radiation is how energy from sun reaches the earth. n

n n n If we double the temperature, the power radiated goes up by 24 =16. If we triple the temperature, the radiated power goes up by 34=81. Note: You must use the Absolute temperature scale

Work Done by a Gas n n n Work=(Force)x(distance) =F y Force=(Presssure)x(Area) W=P(A y) =P V

First Law of Thermodynamics Conservation of energy n When heat is added into a system it can either 1) change the internal energy of the system (i. e. make it hotter) or 2) go into doing work. Q=W + U. Note: For our purposes, Internal Energy is the part of the energy that depends on Temperature.

Heat Engines n If we can create an “engine” that operates in a cycle, we return to our starting point each time and therefore have the same internal energy. Thus, for a complete cycle Q=W

Model Heat Engine Qhot= W+Qcold or n Qhot-Qcold=W n (what goes in must come out)

Efficiency n n We want to write an expression that describes how well our heat engine works. Qhot=energy that you pay for. W=work done (what you want. ) Qcold= Waste energy (money). Efficiency = e = W/Qhot

n n n If we had a perfect engine, all of the input heat would be converted into work and the efficiency would be 1. The worst possible engine is one that does no work and the efficiency would be zero. Real engines are between 0 and 1

Example Calculation n In every cycle, a heat engine absorbs 1000 J from a hot reservoir at 600 K, does 400 J of work and expels 600 J into a cold reservoir at 300 K. Calculate the efficiency of the engine.

Efficiency of Heat Engine A. B. C. D. 2. 5 0. 4 0. 667 0. 3

Example Calculation n In every cycle, a heat engine absorbs 1000 J from a hot reservoir at 600 K, does 400 J of work and expels 600 J into a cold reservoir at 300 K. Calculate the efficiency of the engine. e= 400 J/1000 J=0. 4 This is actually a pretty good engine.

Second Law of Thermodynamics (What can actually happen) Heat does not voluntarily flow from cold to hot. OR n All heat engines have e<1. (Not all heat can be converted into work. ) n

Carnot Engine n n The very best theoretically possible heat engine is the Carnot engine. The efficiency of a Carnot engine depends on the temperature of the hot and cold reservoirs.

Example Calculation Part II n In every cycle, a heat engine absorbs 1000 J from a hot reservoir at 600 K, does 400 J of work and expels 600 J into a cold reservoir at 300 K. Calculate the efficiency of the best possible engine.

Efficiency of Carnot Engine A. B. C. D. 0. 4 0. 5 0. 6 0. 8

Example Calculation Part II n n n In every cycle, a heat engine absorbs 1000 J from a hot reservoir at 600 K, does 400 J of work and expels 600 J into a cold reservoir at 300 K. Calculate the efficiency of the best possible engine. e= 1 -300/600 =0. 5 Recall that the actual engine has e=0. 4.