Processteknikens grunder (”PTG”) Introduction to Process Engineering v.2014 3. Energy conversion, balances, efficiency, equilibrium (Introduction to Thermodynamics) Ron Zevenhoven Åbo Akademi University Thermal and flow engineering / Värme- och strömningsteknik tel. 3223 ; [email protected] Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 1/124 3.1: Energy Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 2/124 What is energy? /1 . ”Energy is any quantity that changes the state of a closed system when crossing the system boundary” (SEHB06) . ”Energy is the capacity to do work” (A83) . ”Energy is the capacity to do work or produce heat” (ZZ03) Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 3/124 What is energy? /2 . Energy cannot be produced or destroyed (First Law of Thermodynamics*) but it can be converted from one form into another, and vice versa. Energy can be degraded to lower quality, as a consequence of producing and converting heat (Second Law of Thermodynamics*) * sv: Termodynamikens Första och Andra Huvudsatsen Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 4/124 Types of energy /1 . In a closed system, energy is . These energies are all relative to a present (”stored”) as reference frame or reference state: potential energy* Ep and . potential energy relative to a kinetic energy** Ek position z = 0 in a gravity field (mechanical energy) and . kinetic energy relative to a non- internal energy*** U moving reference frame with (thermal energy) velocity v = 0 . For a mass m, with vertical . internal energy relative to zero position z in a gravity field and temperature T = 0, or surroundings velocity v defined as temperature T = T°. Ep = m· g· z 2 2 Ek = ½· m· v = ½· m· v U = m·u (* sv: lägesenergi; * * sv: rörelseenergi; Picture: *** sv: inre energi) SEHB06 Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 5/124 Types of energy /2 Unit: Joule, J ; 1 J = 1 N·m= 1 kg·m2/s2 Energy form Energy per unit mass Comment Kinetic energy ½v·v = ½v2 velocity v Potential energy g·z gravity g, height z Internal energy u Pressure energy p/ρ pressure p, density ρ Enthalpy u + p/ρ Surface energy (σ·A) /(ρ·V) surface tension σ surface A, volume V ..... ...... ...... Most important energy forms for (chemical) process engineering Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 6/124 7/124 Potential energy A visualisation of potential energy, showing two mechanical equilibrium points A and C, point C being the most stable, and point B being the most unstable Picture: M62 8/124 Potential energy, kinetic energy 2 2 Conservation of mechanical energy: ½mv1 + mgz1 = ½mv2 + mgz2 2 2 For a closed system with constant mass: ½v1 + gz1 = ½v2 + gz2 Picture: KJ05 Picture: CB98 Transformation kinetic energy ↔ potential energy (without friction !) Internal energy, U /1 . Internal energy U is a consequence of the motion of constituent molecules of a substance and their interactions (T06) . Unit : J . Specific internal energy u = U/m (J/kg) Picture: SEHB06 Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 9/124 Internal energy, U /2 . Internal energy of a material or substance is related to temperature via the specific heat, also referred to as heat capacity, (sv: värmekapacitet) c (unit: J kg-1K-1 or J mol-1K-1) introduced by Gadolin at ÅA, 1784 . Defining u = 0 at reference temperature T° (for example T 0°C or 25°C) gives u = T° ∫ c dT ≈ c· (T – T°) Alternatively, a reference value u = u° can be defined for T T = T° = 0°C or 25°C, then u = u° + T° ∫ c dT As c = c(T), an approxation for c for the temperature range T1 →T2 is c(Taverage) for Taverage = ½(T1+T2) Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 10/124 11/124 Internal energy, U /3 . For gases, a distinction is made between specific Specific heat data for several materials heat at constant volume, cv and specific heat at constant pressure, cp (see below section 3.4) The specific heat ratio cp/cv = γ = κ . Solids and (ideal) liquids are (practically) incompressible: cp= cv = c 12/124 Example: specific heat solids, liquids /1 . An aluminum ball with mass mb= 80 g and temperature Tb = 200°C is dropped into a volume Vw = 6 liters of water that has a temperature Tw = 22°C. The bath is well insulated. Calculate the final temperature Teq of the ball and the water at equilibrium. Consider only internal energy. Specific heat data: cwater = 4.19 J/(g· K); cAl = 0.88 J/(g·K) 13/124 Example: specific heat solids, liquids /2 •Answer: only internal energy needs to be considered; the sphere cools down from Tb to Teq while the water heats up from Tw to Teq. The energy for heating the water comes from cooling the sphere; the internal energy balance gives mw·cw·(Teq-Tw) = mb·cAl·(Tb-Teq) *) 3 3 with mass mw = 0.006 m ·1000 kg/m = 6 kg The unknown temperature Teq is then found after rewriting *) Teq = (mb·cAl·Tb+mw·cw·Tw) / (mw·cw+mb·cAl ) = 22.26°C Total energy of a system . Total energy of a system E = Ek + Ep + U (J) = m· ek + m· ep + m· u (J) with specific energies ek, ep and u (J/kg) . A mass stream m (kg/s) corresponds to an energy stream Ė . Ė = Ėk + Ėp + U = m· (ek + ep + u) (J/s) Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 14/124 3.2: Energy transfer, First Law of Thermodynamics, Work, Power, Heat Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 15/124 Energy transfer . For a closed system ENERGY can be transferred across the boundary by WORK or by HEAT transfer . For an open system, MASS may cross the bounday and the ENERGY associated with that can enter the system, in addition to WORK or by HEAT transfer (as for a closed system) . Generally, for solid matter (”rigid objects”), work changes kinetic energy and potential energy of a system, while heat changes internal energy. For gases and liquids (”fluids”) matters are more complicated: friction in fluid flow gives viscous heat, compression of a gas at constant volume increases its temperature, etc. Picture: KJ05 Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 16/124 First Law of Thermodynamics Also known as the ”conservation of energy” principle . ”The energy of an isolated system is constant” (A83) . Energy can be converted from one form into another, and vice versa for example heat Q can be converted into work W and vice versa - but there are limitations ! (see section 3.6) Closed system ∆E = W + Q (or: dE = δW + δQ) . Open system ∆E = W + Q + min· ein -mout· eout . Energy cannot be produced and speaking about ”energy production” is wrong and silly Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 17/124 Work /1 (sv: arbete) . ”Work is force acting over a distance” (ZZ03) . ”Work is the transfer of energy across a system or control-volume boundary, exclusive of energy carried across the boundary by a flow, and not the result of a temperature gradient at the boundary or a difference in temperature between the system and the surroundings” (T06) . ”Work is mechanical energy in transit” (BB10) Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 18/124 Work /2 (sv: arbete) . ”Work is mechanical energy in transit” (BB10) . ”Work stimulates organised motion” (A83) . Work is a transfer process for mechanical energy . Note: work (a path function) is not a system property . Sign of work W : W > 0 implies work done ON the system; W < 0 implies work done BY the system . In many cases it is defined otherwise (with opposite sign) in engineering calculations (see for example KJ05) ! Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 19/124 20/124 Work /3 . Most important types of work: shaft work (sv: axelarbete), expansion / compression work, electrical work . For a constant force F, moving a body from position s1 to s2 requires work . W12 = F· (s2 –s1) (note vectors!) . For a non-constant force F = F(t) or F = F(s), the work follows from integration over the path: W12 = path ∫ δw = s2 s1∫ F· ds Pictures: KJ05 Work /4 work is a path function! . Work is a path function (an inexact differential) and a differerential ”dw” makes no sense . ”W1” or ”W2” at start / end does not mean anything ! . W = W12 depends on the path from position or state ”1” to position or state ”2” Two paths (top view !) for . It is preferable to use moving a crate against notation δw or đwinstead friction with the floor (but nonethless ”dw” is used in general.....) Picture: KJ05 Åbo Akademi University | Thermal and Flow Engineering | 20500 Turku | Finland 21/124 22/124 Compression/expansion of gas /1 . Assume a frictionless, rigid, perfect-fit piston . inside: a gas . pressure outside = pex pressure inside = pin pex < pin → the piston moves outwards/upwards, doing work (w < 0 ) . δw= Fz· dz = (Fz/A)·(A·dz) Picture: A83 = - pex· dV . For ∆V = V –V : Note: work = force * distance final initial = (pressure*surface) * distance work W = - pex· ∆V = pressure * (surface*distance) = pressure * volume change 23/124 Compression/expansion of gas /2 . The work W = - pex· ∆V can also be shown in a p,V plot or indicator diagram . The work depends on the external pressure; against a vacuum (pex=0) W = 0 To be continued ...... Picture: A83 24/124 Power . Power (sv: effekt, (kraft)) is the rate of doing work .