Entropy

1
Entropy

• Physics 313
• Professor Lee Carkner
• Lecture 17

2
Exercise 16 Entropy

• Total entropy change is sum of each kg of water
• DS mc ln (Tf/Ti) mc ln (Tf/Ti)
• Final temperature of water 50 C 323 K
• DS (4186) ln (323/273) 4186 ln (323/373)
  704 602
• Entropy increases, 2nd law OK
• Entropy of air compression
• DS nc ln (Tf/Ti) nR ln (Pf/Pi)
• DS (34.5)(29.2) ln (330/290) (34.5)(8.31) ln
  (600000/100000) 130.2 514

3
Enthalpy

• Enthalpy (H) is defined as
• What is enthalpy?
• u is the internal energy
• Used in power generation, refrigerators, steam
  systems

4
Specific Enthalpy

• Enthalpy per unit mass is the specific enthalpy
• If we define a flow rate m (kg/s), the total
  power is
• P mh
• Both h and s are tabulated and can often be
  looked up

5
Turbines and Compressors

• Turbine
• Blades turn which turns shaft
• Compressor
• Blades compress a fluid
• The PE and KE of the fluid are generally low, so
  the energy is dominated by enthalpy

6
Turbines
7
Isentropic Processes

• This means that si sf
• May have to extrapolate

8
Isentropic Efficiency

• How close to maximum efficiency is a process?
• Called the isentropic efficiency
• Similar to comparing a engine to a Carnot cycle

9
Isentropic Efficiency Example

• Turbine
• A turbines work depends on the enthalpy so
• where h2 is the actual and isentropic final state
  of the system

10
Cosmic Entropy

• The second law holds for the entire universe
• But, even when things get hotter,
• What about black holes?
• Where will it all end?

11
Cygnus X-1
12
Black Holes

• How does entropy apply to a black hole?
• Energy equals mass (general relativity)
• If a box of gas is thrown in a black hole, the
  entropy of the universe decreases
• Violates second law!

13
Black Holes and Entropy

• Entropy is related to the size of the event
  horizon
• Hot bodies emit radiation
• Black holes aint so black!

14
Hawking Radiation

• How can a black hole emit radiation?
• You can create something out of nothing if you do
  it so fast the universe does not notice
  (uncertainty principle)
• Black holes lose mass

15
Black Hole Temperature

• Since a black hole has entropy, it must have a
  temperature
• Low mass black holes are hotter than high mass
  ones
• For a black hole formed in a supernova the
  minimum mass is about 3 solar masses
• Washed out by 3 K cosmic microwave background

16
Arrows of Time

• Three arrows of time
• Thermodynamic
• Psychological
• Cosmological

17
Entropy and Memory

• Memory requires energy dissipation as heat
• Your head or a hard drive has to get hot

18
Synchronized Arrows

• Why do all the arrows go in the same direction?
• Can life exist with a backwards arrow of time?
• Does life only exist with a forwards arrow of
  time? (anthropic principle)

19
Fate of the Universe

• If the universe has enough mass, its expansion
  will reverse
• Cosmological arrow will go backwards
• Universe seems to be open
• Universe will probably expand forever

20
Heat Death

• Entropy keeps increasing
• Stars burn out
• Can live off of compact objects, but eventually
  will convert them all to heat
• Universe becomes completely random radiation
  field