Transcript Slide 1

CHAPTER 3
BASIC CONCEPTS
OF MASS AND ENERGY
BALANCES
Mass Balance
Variations of mass
contained whitin
the control volume
at time “t”
=
Total mass
flow entering
the system at
time “t”
-
mcv = mi - me
Where :
mcv : mass change
mi : inputs
me: outputs
Total mass
flow leaving
the system at
time “t”
Example : Mass Balance
Mass balance for a system with chemical reaction
A fuel oil is analyzed and is found to contain 87%
weight carbon, 11% hydrogen and 1.4% sulfur, with
the remainder being non-combustible (inert)
material.
• The oil is burned with 20% excess air (based on
complete combustion of the carbon to CO2, the
hydrogen to H2O and the sulphur to SO2). The oil is
burned completely, but 5% of the carbon forms CO
instead of CO2.
• Calculate the molar composition of the exhaust
gas leaving the burner.
Example : Mass Balance
NOTE :
INPUT RATE = Qs * Cs + Qw * Cw
OUTPUT RATE = Qm * Cm = (Qs + Qw) * Cw
DECAY RATE = KCV
INPUT RATE = OUTPUT RATE + DECAY RATE
Energy Balance for Closed Systems
Conservation of energy principle:
Time interval
variation of the
total energy in a
system
=
INPUT
Net energy
transfered across
the system
boundary by heat
transfer into the
system
-
OUTPUT
Net energy
transfered across
the system
boundary by work
done by the
system
Total Energy Variation
KE + PE + U = Q – W
Where :
 KE = Kinetic Energy change
 PE = Gravitational Potential Energy change
 U = Internal Energy change
Q = Heat
W = Work
All parameter mentioned above, are in Joules, Btu or Calories.
Characteristics of Energy
Balance Calculations
– W is the work transfered from the surroundings
to the system.
+ Q is the heat energy transfered into the system
from the surroundings.
Therefore :
+ W is the work done by the system released into
the surroundings
- Q is the heat energy transfered into the
surroundings from the system
Example : Energy Balance
A mixture of 1 kmol of gaseous methane and 2
kmol of oxygen initially at 25°C and 1 atm
burns completely in a closed, rigid container.
Heat transfer occurs until the products are
cooled to 900K. Determine the amount of heat
transfer in kJ.
State 1
State 2
1 kmol CH4 (g)
2 kmol O2
T1= 25°C
P1= 1 atm
Products of
combustion
T2
P2
Example : Energy Balance
Assumptions :
1. The contents of the closed, rigid container are taken
as the system
2. Kinetic, potential energy effects and work = 0.
3. Combustion is complete
4. The reactants and products each form ideal gas
mixtures.
5. The initial and final states are equilibrium states
Example : Energy Balance
Example : Energy Balance