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## CHAPTER 3

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**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” Total massflow leaving the system at time “t” = - mcv = mi - me Where : mcv : mass change mi : inputs me: outputs**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**INPUT OUTPUT Netenergy transfered across the system boundary by workdone by the system Netenergy transfered across the system boundary by heattransfer into the system Conservation of energy principle: Time interval variation of the total energy in a 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 Products of combustion T2 P2 1 kmol CH4 (g) 2 kmol O2 T1= 25°C P1= 1 atm**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