Absolute Zero Physics 313 Professor Lee Carkner Lecture 15

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