ME 200
Thermodynamics
PROF. SHELBY HUTCHENS
Optional Overview – Lessons 6-1 through 6-4
Multi-device Systems Solution Process
1. Determine `knowns’ and `unknowns’
1. Check for the substance model used.
2. Options: stream state, mass flow rate, heat, power (work)
2. Draw system boundaries to minimize the number of
unknowns involved in the mass/energy rate balances
3. Write and solve mass and energy rate balances for the
system boundaries.
‘Known’ states
The state principle: The state of a simple compressible system is fully
determined when any two independent intensive thermodynamic
properties are fixed.
But… for the purposes of integrated systems, the state of a stream is
considered ‘known’ if an enthalpy difference can be determined
between that stream and another stream.
p
For a simple, compressible fluid, the
state is fully determined when any two
intensive thermodynamic properties
are known: v, p, u, h, x, T
v
Substance Model: Data Tables
The state principle
exactly aligns with
determining `knowns’
for multi-device systems.
Substance Model: Ideal Gas
The state principle can
differ from determining
`knowns’ for multidevice systems.
Substance Model: Incompressible Fluid
The state principle
occasionally differs from
determining `knowns’
for multi-device systems.
The tricky case: Low pressure
compressed liquid state
Lesson 6-2, Prob. 12
#"
ℎ! 𝑝!, 𝑇! − ℎ" 𝑝", 𝑇" = ' 𝑐 𝑑𝑇 + 𝑣 𝑝! − 𝑝"
#!
Multi-device systems: ‘Known’ states
Assumptions given by the
problem statement:
• Steady-state
• Negligible pressure drop
in water stream
• c is constant for water
Find:
• The mass flow rate of
water, 𝑚̇ !
• The pressure in stream 2
The state of a stream is considered ‘known’ if an enthalpy difference
can be determined between that stream and another stream of
‘known’ state.
R-134a vapor dome
p
v
Multi-device systems: boundaries
Assumptions given by the
problem statement:
• Steady-state
• Negligible pressure drop
in water stream
• c is constant for water
Find:
• The pressure in stream 2
• The mass flow rate of
water, 𝑚̇ !
Energy rate balance to find the pressure
of stream 2
𝑑𝐸
= 𝑄̇ − 𝑊̇ + * 𝑚̇ !" ℎ!" − * 𝑚̇ #$% ℎ#$%
𝑑𝑡
!"
#$%
Energy rate balance to find the mass flow
rate of water
𝑑𝐸
= 𝑄̇ − 𝑊̇ + * 𝑚̇ !" ℎ!" − * 𝑚̇ #$% ℎ#$%
𝑑𝑡
!"
#$%