Second Law of Thermodynamics Physics 202 Professor Lee Carkner Lecture 18

PAL #17 Entropy  Temperature of Titan   P in = (F)(  )(r 2 ) = (15.18)(  )(2.58X10 6 ) 2 = 3.17X10 14 W   T = [(P in )/(  A)] 1/4 = [(P in )/(  4  r 2 )] 1/4  T = [(3.17X10 14 )/((5.6703X10 -8 )(4)(  )(2.58X10 6 ) 2 )] 1/4 

PAL #17 Entropy (con’t)  Minimum mass molecule that will stay in atmosphere ((  m = (300kTR)/(2GM)  m = [(300)(1.38X )(90)(2.58X10 6 )]/ [(2)(6.67X )(1.35X10 23 )]  m = 5.33X kg   What gasses would not be found on Titan?   H 2, mass = 2, no   CH 4, mass = 16, no  CO 2, mass = 44, yes

Hero’s Door Opener (1 AD)

Steam Engines (18th century)

Internal Combustion Engine (late 19th century)

Engines   These processes can be adiabatic, isothermal etc.   Engines have a working substance that transfers heat and does work (usually a gas)  The four processes will bring the working substance back to its initial condition

p-V and T-S Engine Diagrams

Engine Elements

The Stirling Engine   The engine consists of two pistons one of which is maintained at a high temperature T H, the other at a low temperature T C   The pistons are connected to linkages to transfer out the work

Stirling Engine Diagram QHQH QCQC THTH TCTC Hot Piston Cold Piston

The First 2 Strokes  1)  The hot piston moves up adding heat Q H to the gas  2)  Hot piston moves down and cold piston moves up, pushing hot gas into the central chamber

The Last 2 Strokes  3)  The cold piston moves down transferring heat Q C to the cold reservoir  4)  The cold piston moves down and the hot piston moves up, drawing the cold gas back into the hot piston

Stirling Engine Diagram

Cycle Computations   Example: What is the net work of the Stirling Engine?  For the first isothermal expansion:   For the isothermal compression:   Net work equals W out –W in 

Heat and Work  Over the course of one cycle positive work is done and heat is transferred   Since the engine is a cycle the change in internal energy is zero  Let us now use a Carnot engine (sometimes called an ideal engine), which has the maximum efficiency   Since the total heat is Q H -Q L from the first law of thermodynamics  W = Q H -Q L

Efficiency   In order for the engine to work we need a source of heat for Q H   = W/Q H  An efficient engine produces a high ratio of output work to input heat

Efficiency and Heat   = 1 - (Q L /Q H )  Q H = W + Q L

Efficiency and Entropy   If all the processes are reversible, the change in entropy between the two reservoirs must be zero so: Q H /T H = Q L /T L   C = 1 - (T L /T H )   Called ideal or Carnot engines

Ideal and Perfect Engines  The above equations hold only for ideal engines   Since no real processes are truly ideal  <  C   It is also impossible to produce an engine where Q H is completely converted into work  Why?   Called a perfect engine (no energy lost to heat)  Perfect engines violate the 2nd law of thermodynamics but not the first

Perfect Engine

Entropy and Real Engines   Engines get hot, they produce waste heat (Q L )   The first law can be written:   The second law of thermodynamics can be stated:  You can not get out of an process as much as you put in