L20_Energy_Balance - Energy Balance­Overall 10/13/11 1...

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Unformatted text preview: Energy Balance­Overall 10/13/11 1 LEARNING OBJECTIVES By the end of this topic, you should be able to understand the following: • • • • Definition of Energy Conservation of Energy Form of Energy Energy Balance for Closed and Open Systems 10/13/11 2 CONSERVATION OF ENERGY The law of conservation of energy states that for any process unit (s), energy can neither be created nor destroyed but it can change from one form to another forms of energy. The law concludes that at a steady state: Total energy INPUT = Total energy OUTPUT 10/13/11 3 FORM OF ENERGY There are 6 forms of energy Work (W) Heat (Q) Kinetic energy (Ek) Potential energy (Ep) Internal energy (U) Enthalpy (H) 10/13/11 4 FORM OF ENERGY Work (W)- form of energy that represent a transfer form between the system and surroundings. Work can not stored. Work is positive when done on the system. For example, work done by piston. state 2 W= ∫ Fds state1 10/13/11 5 FORM OF ENERGY Heat (Q)- heat flow or total energy flow across a Heat system boundary that is caused by a temperature difference between the system and the surroundings. Heat is not stored nor created. Heat is positive when transferred to the system via conduction, convection or radiation. Q = UA∆T U=overall heat tranfer coefficient, A=surface area, T=temperature 10/13/11 6 FORM OF ENERGY Internal Energy (U)- due to; motion of molecules relative to the centre motion of mass of the system, rotational, vibrational, and electromagnetic rotational, interactions of molecules, and interactions of the atomic and subatomic interactions constituents of the molecules constituents T2 U 2 − U1 = ∫ UCV dT T1 10/13/11 7 FORM OF ENERGY KINETIC AND POTENTIAL ENERGY 1 Ek = mu 2 2 s The kinetic energy portion is defined by s Thus you could calculate the kinetic energy of a portion of fluid with mass m (kg) and uniform velocity u (m/s). s Now, for potential energy, E p = mgz where z = height of the object above a reference plane (potential energy is assigned as 0) 10/13/11 8 FORM OF ENERGY Enthalpy (H)- the summation of internal energy and the multiplication of pressure with volume H = U + pV 10/13/11 9 CLOSE AND OPEN SYSTEMS CLOSE AND OPEN SYSTEMS Closed system or non-flow system- no transfer of mass across the boundary Open system or flow system- exchange of mass occurs across the boundary 10/13/11 10 CLOSE AND OPEN SYSTEMS CLOSE AND OPEN SYSTEMS s For a simple and closed system, energy may enter or For leave a closed system in only two ways: leave – As heat: a flow of heat into the system is a positive flow, a As flow out is negative. flow – As work: thus the application of a force, torque, or voltage. As In this text, work, is positive when it is done on the system. s All of our energy balances is based on the first law of All thermodynamics, known as the conservation of thermodynamics known energy law (similar to conservation of mass law neither can be created nor destroyed). 10/13/11 11 ENERGY BALANCES ENERGY BALANCE FOR CLOSED SYSTEMS s The balance: Final energy of syst. = initial energy of syst. + net energy Final transferred to syst. transferred • • • s Initial energy of the system = Ui + Eki + Epi Initial Final energy of the system = Uf + Ekf + Epf Final kf Energy transferred = Q - W (heat energy transferred minus work done) Hence Hence Uf + Ekf + Epf = Ui + Eki + Epi + Q - W kf Rearranging (Uf - Ui) + (Ekf - Eki) + (Epf - Epi) = Q – W kf pf Simplify U + Ek + Ep = Q – W “first law statement for a closed system” 10/13/11 12 ENERGY BALANCES ENERGY BALANCE FOR CLOSED SYSTEMS s The internal energy - dependent upon chemical composition, state of The aggregation, and temperature. If no changes in T, phase, or aggregation, no chemical composition occur: chemical U0 s Well insulated syst., or the outside temp. is the same as the system, Well Q = 0 termed as adiabatic, no heat exchanged. adiabatic no s Work done on the system can be done by a piston (compressing, Work exerting force), a propeller, or by an electric current. If none of these things are done W=0 10/13/11 13 ENERGY BALANCES ENERGY BALANCE FOR OPEN SYSTEMS s The previous equations applied to closed syst., that is, syst. in The which mass were conserved. What about an open system where mass does cross the boundaries of the system? mass s In an open system, several other "things" can impact the energy. In Have work done by propeller, called "shaft" work. s There is also "flow" work; the work done on the fluid as it enters There the system minus the work done by the fluid at the outlet. the s This "flow" work is calculated by looking at the pressure P and This • volumetric flow rate, V volumetric s • • • Thus, Wfl (N.m/s) = Pout (N/m ) * Vout (m /s) - Pin (N/m ) * Viin (m3/s) Thus, /s) n (m 10/13/11 2 3 2 14 ENERGY BALANCES ENERGY BALANCE FOR OPEN SYSTEMS s Another property of the energy balance for an open system is: ^ ^ ^ H =U +P V s Note the symbol ^ on top of the letter H, U and V. This is a Note symbol to represent a specific property. symbol s A specific property is obtained by dividing an extensive property specific by the total amount of the stream. s Thus, if the volume of a stream is 500ft3 and the mass is 100lbm, 5 ft3/Ibm . You can do this for then the specific volume would be then You other properties, including kinetic energy. 10/13/11 15 ENERGY BALANCES ENERGY BALANCE FOR OPEN SYSTEMS s Pages 322, 323 and 324 go through the derivation. You should Pages DEFINITELY look at this, but I won't go through the derivation. The end result is 7.4-15, on pg. 324. • • • Δ H + ∆ Ek + ∆ Ep = Q + Ws s You can see that the difference between an open and closed You system is that we use enthalpy instead of internal energy. 10/13/11 16 Conclusions You have learnt ­Definition of Energy ­Conservation of Energy ­Form of Energy ­Energy Balance for Closed and Open Systems 10/13/11 17 ...
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