Entropy Physics 313 Professor Lee Carkner Lecture 17

Exercise #16 Entropy  Total entropy change is sum of each kg of water:   S = mc ln (T f /T i ) + mc ln (T f /T i )  Final temperature of water = 50 C = 323 K   S = (4186) ln (323/273) ln (323/373) = 704 – 602 =   Entropy increases, 2nd law OK  Entropy of air compression   S = nc ln (T f /T i ) + nR ln (P f /P i )   S = (34.5)(29.2) ln (330/290) – (34.5)(8.31) ln (600000/100000) = – 514 = 

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

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

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

Turbines

Isentropic Processes   This means that s i = s f   May have to extrapolate

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

Isentropic Efficiency Example  Turbine:   A turbines work depends on the enthalpy so:   where h 2 is the actual and isentropic final state of the system 

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?

Cygnus X-1

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!

Black Holes and Entropy   Entropy is related to the size of the event horizon   Hot bodies emit radiation  Black holes ain’t so black!

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

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

Arrows of Time  Three arrows of time:  Thermodynamic   Psychological   Cosmological 

Entropy and Memory   Memory requires energy dissipation as heat   Your head or a hard drive has to “get hot”

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)

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

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 