Lec 3: Conservation of mass continued, state postulate, zeroth law, temperature

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Lec 3 Conservation of mass continued, state
postulate, zeroth law, temperature

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• For next time
• Read 10-1 to 10-2, 10-4 to 10-5, and 2-5 to
  2-8.
• Outline
• Conservation of mass example problems
• Equilibrium and states
• Zeroth law of thermodynamics
• Important points
• Problem solving methodology
• State, path, and process
• Temperature scales

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Review
where
and
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Steady flow
Flows are steady if any derivative with respect
to time equals zero
The term steady state may also be used, which
simply means that any property (used to define a
state) does not vary with time, although they may
vary with position.
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Conservation of mass
If we limit ourselves to steady-state devices
with one entrance and one exit,
OR
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Look at some simplifying cases
Incompressible pipe flow
General Incompressible
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One more simplifying case
Ideal gas incompressible
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TEAMPLAY
Steam enters a turbine with a specific volume of
0.831 ft3/lbm with a velocity of 21.0 ft/s and
leaves with a specific volume of 175.8 ft3/lbm.
The turbine inlet area is 1 ft2 and the outlet
area is 140 ft2. A) What is the mass flow
(lbm/hr)? B) What is the exit velocity (ft/s)?
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Review--State

• The state of a system is defined by the values of
  its properties.

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TEAMPLAY

• How many properties can you name that apply to
  the gas in a high pressure cylinder of nitrogen?
• How many are independent and how many are
  dependent?

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Equilibrium

• A system is in equilibrium if its properties are
  not changing at any given location in the system.
  This is also known as thermodynamic
  equilibrium or total equilibrium.
• We will distinguish four different subtypes of
  thermodynamic or total equilibrium.

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Types of thermodynamic equilibrium

• Thermal equilibrium--temperature does not change
  with time.
• Mechanical equilibrium--Pressure does not change
  with time.
• Phase equilibrium--Mass of each phase is
  unchanging with time.
• Chemical equilibrium--molecular structure does
  not change with time.

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Equilibrium

• Equilibrium implies balance--no unbalanced
  potentials (driving forces) in the system.

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State Principle or State Postulate

• Text says, The state of a simple compressible
  system is completely given by two independent,
  intensive properties.
• Properties are independent if one can be constant
  while the other varies.
• This only applies at equilibrium.

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Process

• Change in state of a system from one equilibrium
  state to another.

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Path
Series of states through which a system passes.
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Properties at end points are independent of the
process
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Constant property processes

• The prefix iso is used to indicate a property
  that remains constant during a process
• Isothermal is constant temperature
• Isobaric is constant pressure
• Isochoric or isometric is constant volume

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Review definitions

• Steady state--any property (used to define a
  state) does not vary with time, although it may
  vary with position.
• Compare with definition of equilibrium. A system
  is in equilibrium if its properties are not
  changing at any given location in the system.
• So, the question arises how does something
  change with time?

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Quasiequilibrium Process
Incremental masses removed during an expansion of
the gas or liquid
Idealized process in which the departure from
equilibrium is infinitesimally small.
Gas or liquid system
Boundary
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Quasiequilibrium Processes

• Engineers are interested in quasiequilibrium
  processes for two reasons
• They are easy to analyze because many
  (relatively) simple mathematical relations apply.
  
• It will be shown later that devices produce
  maximum work or require minimum work when they
  operate on quasiequilibrium processes.

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Cycle
Series of processes where the initial and final
states are the same.
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State Principle (more rigorous definition)

• The number of independent, intensive properties
  needed to characterize the state of a system is
  n1 where n is the number of relevant
  quasiequilibrium work modes.
• This is empirical, and is based on the
  experimental observation that there is one
  independent property for each way a systems
  energy can be independently varied.

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State Principle continued

• The 1 is for heat transfer (Q).
• The n is the number of relevant
  quasiequilibrium work modes. In this course, we
  will usually have n 1.

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Simple system
A simple system is defined as one for which only
one quasiequilibrium work mode applies.
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For a simple system,

• We may write p p(v,T)
• Or perhaps v v(p,T).

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Forms of Energy

• Energy is usually symbolized by E, representing
  total energy
• e is energy per unit mass

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Forms of Energy

• Macroscopic forms--possessed with respect to some
  outside reference frame.
• Kinetic energy,
• Potential energy,

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Forms of energy

• Microscopic forms are called internal energy
  (internal to the molecule) and represent the
  energy a molecule can have as it translates,
  rotates, and vibrates. There are other
  contributors--nuclear spin, for example--as well.
• We will not concern ourselves with the details,
  but will use the symbols U and u.

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Energy

• Now, we have
• and for stationary, closed systems, ?KE and ?PE
  are 0.
• So, for stationary closed systems, ?E ?U

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Energy

• Sensible energy--the portion of the internal
  energy associated with all forms of kinetic
  energy of the molecules.
• Latent energy--refers to internal energy
  associated with binding forces between molecules.
  Phase changes, such as vaporizing (boiling)
  water are latent energy changes.

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Thermal Equilibrium

• Occurs when two bodies are at the same
  temperature T and no heat transfer can occur.

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Zeroth Law of Thermodynamics

• If two bodies are in thermal equilibrium with a
  third body, they are in thermal equilibrium with
  each other.

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We Need to Work With Temperatures
ºC ºF K R
Boiling point 100 212 373.15
71.67
Ice point 0.00 32.00 273.15
491.67
Absolute Zero -273.15 -459.67
0 0
Triple point _at_ 0.006 atm, T 0.01 ºC
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Temperature relationships

• T (ºR) T (ºF) 459.67 use 460
• T (K) T (ºC) 273.15 use 273