Carnot Thermodynamics Professor Lee Carkner Lecture 12

PAL # 11 Second Law  Refrigerant 134a flowing through a condenser  Heat output of condenser is equal to the change in enthalpy of fluid  Q H =  h 1 = kJ/kg (superheat vapor, Table A-13)  h 2 = kJ/kg (saturated liquid, Table A-12)  Q H = (0.018)( ) =  COP = Q H /W = 3.164/1.2 =  Q L = Q H – W = – 1.2 =

Reversible  A reversible process:   has a net heat and work exchange for all systems as zero   is the theoretical limits for a process 

Irreversible  An irreversible process can be due to:  Friction   Unrestrained expansion of a gas into a vacuum   Heat transfer through temperature difference 

Achieving Reversibility   Heat transfer through a very small temperature differential dT becomes reversible as dT approaches zero  Example Isothermal Work:   dT always very small

The Carnot Cycle  The Carnot engine consists of all reversible processes and thus is the most efficient  Carnot Cycle    An adiabatic fall from T H to T L   Adiabatic process is frictionless and isothermal process has very small temperature differentials

Carnot Cycle

Carnot Principles   All Carnot engines operating between two heat reservoirs have the same efficiency  While we cannot build a real Carnot engine, it gives us the upper limit for the efficiency of a real engine

Carnot Efficiency  The efficiency of a reversible engine depends only on the temperatures of the reservoirs  th,rev = 1 – (T L /T H )   Maximum efficiency for any real engine  Can increase the efficiency of any engine by:  

Kinds of Engines

Quality of Energy   Since work is what we want, we can say that high temperature sources have higher quality energy than low temperature sources   Quality is different from quantity 

Efficiency and Temperature

Carnot Refrigerator  We can also make the same determination for the efficiency of the Carnot refrigerator or heat pump  COP R = 1 / (T H /T L -1) COP HP = 1 / (1 – T L /T H )   Smaller temperature difference means more efficiency 

Carnot Refrigeration Cycle

Kinds of Refrigerators

Heating a House

Thermodynamic Temperature Scale   The efficiency of any engine depends on the ratio of the heats  Thus we can determine the temperature of two reservoirs by measuring the heat flow in and out of an ideal engine operating between them

Kelvin Scale   If assign a magnitude to the degree size we get a complete temperature scale, independent of any substance in a thermometer   Note that we don’t actually use an engine to find T

Perpetual Motion   1st kind:  Machine that creates energy   2nd kind:  Machine that converts heat completely into work   3rd kind:  Machine with no dissipation 

Next Time  Read:  Homework: Ch 6, P: 131, 138, Ch 7, P: 29, 37