Second Law Thermodynamics Professor Lee Carkner Lecture 11

PAL # 10 Flow Devices  Argon gas in a turbine, want temperature of exit gas  Energy balance between enthalpy, ke and work  Input = Output   Mass flow rate  P v = RT  v = RT 1 /P 1 = (0.2081)(723) / (900) =  m’ =  1 A 1 V 1 = (1/ v 1 )A 1 V 1 = (1/0.167)(0.006)(80) =

PAL # 10 Flow Devices  Want to find  h = c p  T   h =   h = (250/2.874) – [(80 2 /2) – (150 2 /2)] / 1000   h =   T =  h/c p = / =  Input T is 450 C so output T is C

The Second Law of Thermodynamics   Processes have preferred directions  Example: melting an ice cube   Energy has a quality as well as a quantity   A tank of gasoline contains highly useful energy, a slightly warmer atmosphere contains fairly useless energy

Heat Reservoir   Something with a large mass or specific heat   Allows for heat transfer at constant T 

Heat Engine  Work can be converted to heat directly  e.g.  Heat can only be converted to work with special devices  In general:   Need a fluid called the working substance 

Engine Notation  Four basic engine properties (all positive):   Output heat to cold reservoir, Q L   Work needed for compression, W in  Some of the output work is needed to run the cycle and thus the net work is:  A cycle has  U = 0, so: W net,out = Q H – Q L

Efficiency  We want to maximize net output work for a given input heat   Called the thermal efficiency  Can express as: 

Refrigerators   Instead of using a temperature difference to create work, uses work to create a temperature difference 

Refrigerator Cycle  Expanding a gas obviously does work   Need a refrigerant undergoing a vapor- compression refrigeration cycle:   Fluid is compressed to high pressure   Expansion valve returns the fluid to low pressure and is moved to the cold chamber

Coefficient of Performance  We want to move the most heat out of the cold chamber for the least work  Since energy is conserved: W net,in + Q L = Q H   Thus:  Can be greater than one

Heat Pump  A heat pump is just a refrigerator with the inside of your house as the hot chamber and the outside as the cold chamber  We want a lot of heat added to the house for a little work  Note that, COP HP = COP R + 1 

Air Conditioner   Uses same COP as refrigerator   For every 2-3 joules of heat removed from cold chamber, need about 1 joule of work

Kelvin – Planck Statement  Why does an engine have to have Q out ?   We need to compress the gas back to the initial state and that requires an output of heat  Kelvin – Planck Statement:   Means that  th is always less then one

Clausius Statement   It is impossible for a cyclic device to move heat from cold to hot with no input work 

Equivalence   A perfect engine powering a refrigerator will make it perfect as well 

Next Time  Read:  Homework: Ch 6, P: 28, 78, 91, 97