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Absolute Zero
Physics 313Professor Lee
CarknerLecture 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/QH = 0.6
Can get output heat from first law QL = QH - W = 14043-8426 = 5617 J
Carnot and Temperature How are the heat exchanges related to the
temperature? For ideal gas:
QH/QL = TH/TL [(ln V2/V3)/ln V4/V1)]
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 TL, you lower QL
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 TH and decreasing TL 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 = CVdT +PdV
S = CV (dT/T) + nR (dV/V)
Similarly for:
S = n cP (dT/T) - nR ln (Pf/Pi)
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