 # Engines Physics 202 Professor Lee Carkner Lecture 16.

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Engines Physics 202 Professor Lee Carkner Lecture 16

PAL #15 Entropy  1 kg block of ice (at 0 C) melts in a 20 C room   S = S ice + S room  S ice = Q/T = mL/T = [(1)(330000)]/(273)  S ice =  S room = Q/T = -330000/293  S room =   S = +1219.8 – 1136.5 =  Entropy increased, second law holds

PAL #15 Entropy  Entropy of isobaric process, 60 moles compressed from 2.6 to 1.7 ms at 100 kPa   S = nRln(V f /V i ) + nC V ln(T f /T i )   T i = (100000)(2.6)/(60)(8.31) =521 K  T f = (100000)(1.7)/(60)(8.31) = 341 K    S = -530 J/K  Something else must increase in entropy by more than 530 J/K 

Engines   General engine properties:  A working substance (usually a gas)   A net output of work, W   Note that we write Q and W as absolute values

The Stirling Engine  The Stirling engine is useful for illustrating the engine properties:   The input of heat is from the flame   The output of heat makes the cooling fins hot

Heat and Work   How does the work compare to the heat?   Since the net heat is Q H -Q L, from the first law of thermodynamics:  E int =(Q H -Q L )-W =0 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 converts as much of the input heat as possible into work  The rest is output as Q L

Efficiency and Heat   = 1 - (Q L /Q H )  Q H = W + Q L  Reducing the output heat means improving the efficiency

The Second Law of Thermodynamics (Engines)   This is one way of stating the second law: It is impossible to build an engine that converts heat completely into work   Engines get hot, they produce waste heat (Q L )  You cannot completely eliminate friction, turbulence etc.

Carnot Efficiency   C = 1 - (T L / T H )  This is the Carnot efficiency   Any engine operating between two temperatures is less efficient than the Carnot efficiency  <  C  There is a limit as to how efficient you can make your engine

The First and Second Laws   You cannot get out more than you put in   You cannot break even  The two laws imply:   W < Q H   W  Q H

Dealing With Engines  W = Q H - Q L  = W/Q H = (Q H - Q L )/Q H = 1 - (Q L /Q H )   C = 1 - (T L /T H )  If you know T L and T H you can find an upper limit for  (=W/Q H )  For individual parts of the cycle you can often use the ideal gas law: PV = nRT

Engine Processes   We can find the heat and work for each process   Net input Q is Q H  Net output Q is Q L   Find p, V and T at these points to find W and Q

Carnot Engine   A Carnot engine has two isothermal processes and two adiabatic processes   Heat is only transferred at the highest and lowest temperatures