Absolute Zero Physics 313 Professor Lee Carkner Lecture 15

Exercise #14 Carnot Cycle  Isothermal heat = work   W = (1.5)(8.31)(700)ln(2X10 -3 /4X10 -4 )   Net work depends of efficiency   = W/Q H = 0.6   Can get output heat from first law   Q L = Q H - W = = 5617 J

Carnot and Temperature  How are the heat exchanges related to the temperature?   For ideal gas: Q H /Q L = T H /T L [(ln V 2 /V 3 )/ln V 4 /V 1 )]  The volume term equals 1 (can relate V’s from the adiabatic processes) 

Temperature Scale  Temperature can be related to the heat transfers of a Carnot engine    Using the triple point of water  Called the thermodynamic temperature   Can make a “Carnot Thermometer” by running a Carnot engine at unknown T and T for triple point of water 

Absolute Zero  If you lower T L, you lower Q L   Defines absolute zero   Absolute zero defined this is way is:  

Efficiency  Can write the efficiency of a Carnot engine as:    Increase the efficiency by increasing T H and decreasing T L  ro  For a Carnot refrigerator the coefficient of performance is:

Entropy  The limits on efficiency for engines and refrigerators are expressions of entropy    Entropy represents a preferred direction for processes 

Heat and Temperature  We saw that:  If we include the signs of the heat:  This is true for any Carnot cycle  Any curve can be represented as the sum of many Carnot cycles 

Entropy Defined  For any reversible cycle:   The integral along any reversible (non- closed) path represents the change in entropy: dS = dQ/T

Creating Entropy  How might we change the entropy of a system  Consider work done on a substance in contact with a heat reservoir at temperature T    The ratio of work to the temperature of the reservoir is the entropy change   Note:  

Ideal Gas Entropy  To calculate entropy need expression for dQ dQ = C V dT +PdV  S =  C V (dT/T) +  nR (dV/V)   Similarly for:  S = n  c P (dT/T) - nR ln (P f /P i )

T and S  Heat can be expressed as:  Heat is the area under the curve on a TS diagram  

The TS Diagram  How are standard processes plotted on a TS diagram?  Isotherm   Adiabatic   No entropy change, so vertical line 

Other Processes  Isobar  Curved line with slope:   Isochor  Curved line with slope:  

TS Diagram S T Isotherm Isentrope Isobar Isochor

Entropy and Isotherms  We write change in entropy as:   If T is constant   The change in entropy for an isothermal process depends only on the temperature and the total heat exchange 