1. BASIC CONCEPTS OF MASS AND ENERGY BALANCES
CHAPTER 3
BASIC CONCEPTS
OF MASS AND ENERGY BALANCES
Narration : this chapter will review the basic concepts of mass and energy balances.

2. Mass Balance mcv = mi - me = -
Variations of mass contained whitin the control volume at time “t”
Total mass flow entering the system at time “t”
Total mass flow leaving the system at time “t” = -
mcv = mi - me
Narration : The following equation describes the mass balance calcualations. This expression includes input and output rates, as well as decay and accumulation rates
Where :
mcv : mass change
mi : inputs
me: outputs

3. 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.

4. 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
Narration : This slide demonstrates how excel can be used to solve this problem instead of solving manually.

5. Energy Balance for Closed Systems
Conservation of energy principle:
INPUT
OUTPUT
Net energy transfered across the system boundary by heat transfer into the system
Net energy transfered across the system boundary by work done by the system
Time interval variation of the total energy in a system = -
Narration : In order to perform an energy balance on a closed system, one must keep in mind the principle of conservation of energy. If no energy enters or leaves the system, the variation of the total energy will remain 0, however if there is a difference, the variation will indicate it, and in which direction the energy is flowing.

6. 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
Narration : This equation, based on the first law of thermodynamics, enables anyone to assess the energy fluxes over a determined boundary.
All parameter mentioned above, are in Joules, Btu or Calories.

7. 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
Narration : The algebraic signs must be considered as a convention when performing energy balance equations.

8. 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

9. Example : Energy Balance
Assumptions :
The contents of the closed, rigid container are taken as the system
Kinetic, potential energy effects and work = 0.
Combustion is complete
The reactants and products each form ideal gas mixtures.
The initial and final states are equilibrium states
Narration : the following assumptions need to be followed in order to be able to solve this problem

10. Example : Energy Balance
Narration : these images (this and following slide) demonstrate how to use excel in order to solve this problem.

11. Example : Energy Balance
Narration : Therefore, in this situation the heat (energy) transfer is made to the surroundings from the system’s combustion. (note the sign)