Engines Physics 202 Professor Lee Carkner Lecture 18

Notes  We should have class Friday, Jan 27  But check web page first  Exam #2 has been moved from next Monday to next Wednesday (Feb 1)  The discussion questions that were ed out Monday are due Friday in class

PAL #16 Internal Energy  3 moles of gas, temperature raised from 300 to 400 K  He gas, isochorically  Q = nC V  T, C V =  Q = (3)(3/2)R(100) =  # 4 for heat, all in translational motion  He gas, isobarically  Q = nC P  T, C P =  Q = (3)(5/2)R(100) =  # 2 for heat, energy in translational and work  H 2 gas, isochorically  Q = nC V  T, CV =  Q = (3)(5/2)R(100) =  # 2 for heat, energy into translational and rotational motion  H 2 gas, isobarically  Q = nC P  T, CP =  Q = (3)(7/2)R(100) =  # 1 for heat, energy, into translation, rotation and work

Engines   General engine properties:  A working substance (usually a gas)   An output of work 

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 fins hot

Parts of the Cycle  Cycle can be broken down into specific parts  In general:   One involves compression   One involves the output of heat Q L   Change in internal energy is zero

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   E int =(Q H -Q L )-W =0 W = Q H - Q L

Engine Elements

Efficiency  We get work out of an engine, what do we put into it?   Q H is what you put in, W is what you get out so the efficiency is:  = W/Q H   The rest is output as Q L

Efficiency and Heat   = 1 - (Q L /Q H )  The efficiency depends on how much of Q H is transformed into W and how much is lost in 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 Engine   C = 1 - (T C / 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  The first law of thermodynamics says:   The second law of thermodynamics says:   The two laws imply:   W < Q H   W  Q H

Dealing With Engines  Most engine problems can be solved by knowing how to express the efficiency and relate the work and heats: W = Q H - Q L  =  Efficiency must be less than or equal to the Carnot Efficiency:   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:

Entropy   How can we quantify these limits and define a second law?   In any thermodynamic process that proceeds from an initial to a final point, the change in entropy depends on the heat and temperature, specifically:  S = S f –S i = ∫ (dQ/T)

Isothermal Entropy  In practice, the integral may be hard to compute   Let us consider the simplest case where the process is isothermal (T is constant):    This is also approximately true for situations where temperature changes are very small 

Entropy Change  Imagine now a simple idealized system consisting of a box of gas in contact with a heat reservoir    If the system loses heat –Q to the reservoir and the reservoir gains heat +Q from the system isothermally:   The total change in entropy is zero

Second Law of Thermodynamics (Entropy)  This situation is actually an upper limit   S>0  This is also the second law of thermodynamics 