ChemE 260 Work and Heat Dr. William Baratuci Senior Lecturer Chemical Engineering Department University of Washington TCD 4: A & B CB 3: 1 – 4, pg 150 - 155 April 11, 2005

Work Definition Boundary Work or PV Work: F = P A A force acting through a distance A restraining force is overcome to move an object Boundary Work or PV Work: F = P A Thermodynamic Definition of Work Work is done by a system on its surroundings if the sole effect of a process on its surroundings could have been raising a weight. This definition allows for other forms of work, such as spring work, electrical work gravitational work and acceleration work. Baratuci ChemE 260 April 11, 2005

Sign Convention for Work increases as T increases, so changes in have a natural sign. This is not true for work A system can do work on the surroundings or the surroundings can do work on the system We choose which is positive and which is negative. We choose a sign convention. In this course we choose work done BY the system on the surroundings to be positive Always include an arrow for work on our sketches to indicate the sign convention we are using. System WORK Baratuci ChemE 260 April 11, 2005

Power & Path Variables Power: the rate at which work is done Exact Differentials State variables: U  dU Changes in state variables, like U, do not depend on which process path the system follows between 2 states Inexact Differentials Path Variables: W  W Systems do not have work Work is a form of energy that only exists as it moves across a system boundary. W12 depends on the path the process follows from state 1 to state 2. Use  instead of d for inexact differentials of path variables Baratuci ChemE 260 April 11, 2005

Boundary Work and Process Paths 1 2 3 P2 > P1 V2 < V1 T2 > T1 Adiabatic Compression Q = 0 Isochoric Cooling P2 > P3 > P1 V3 = V2 T3 = T1 P1, V1, T1 1 A 3 Isochoric Cooling Adiabatic Compression Q = 0 P3 > P1 > PA V3 < V1 T3 = T1 PA < P1 VA = V1 TA < T1 Consider the two processes shown here: 1-2-3 and 1-A-3 U, H and V are the same for each of these processes because they begin and end at the same states. But, is the amount of boundary work the same for both processes ? The easiest way to tell is to plot the process path on a PV Diagram Then, make use of the fact that boundary work is the integral of P dV to determine if the boundary work done by the two processes are the same. P1, V1, T1

Process Paths on a PV Diagram 2 3 P 1 T2 T1 TA A V ~ Baratuci ChemE 260 April 11, 2005

Boundary Work on a PV Diagram 2 3 P 1 T2 The shaded area is the boundary work done during the process 1-2-3. Is this work positive or negative under our sign convention ? T1 TA A V ~ Baratuci ChemE 260 April 11, 2005

Boundary Work on a PV Diagram 2 3 P 1 T2 The shaded area is the boundary work done during the process 1-A-3. Is this work positive or negative under our sign convention ? The amount of boundary work is NOT equal for the two processes ! This is because work depends on the process path. Work is a PATH variable, NOT a property or state variable like V, U and H. What about heat ? Is the heat transfer for the two processes the same ? Nope. Heat is also a PATH variable. T1 TA A V ~ Baratuci ChemE 260 April 11, 2005

Quasi-Equilibrium Processes Does it matter how rapidly we compress the gas in steps 1-2 and A-3 ? Yes ! When a gas is rapidly compressed… The molecules cannot get out of the way of the piston rapidly enough As a result, the local pressure right in front of the piston is greater than the pressure in the bulk of the gas. Presist > Pbulk As a result, Pfast > Pslow Quasi-Equilibrium Processes Infinitely slow Always in an equilibrium state, Presist = Pbulk Baratuci ChemE 260 April 11, 2005

Wb for Special Types of Processes Isobaric: Isothermal & IG: Polytropic:  = 1: isothermal !   1: Polytropic & IG: Isobaric is the easiest type of process when it comes to evaluating the boundary work. Evaluating Wb for an isothermal process isn’t easy unless the fluid in the system is an ideal gas. Then, it isn’t bad at all Notice that the last equality is true because P1V1 =P2V2 for an IG undergoing a polytropic process.

Heat: Q Another form of energy in transition across a system boundary, like work. Flows spontaneously from “hot” to “cold” Heat is the flow of thermal energy while U is the amount of thermal energy a system holds. Heat is comparable to electrical current while U is comparable to electrical potential or voltage. Sign Convention: Heat flow into a system > 0 Baratuci ChemE 260 April 11, 2005

Heat: A Few Details Heat is a path variable and the differential of heat is inexact, so we use : In an adiabatic process Q = 0 If the heat transfer rate, , is constant, then: Heat Flux: Baratuci ChemE 260 April 11, 2005

Conduction Fourier’s Law: k = thermal conductivity [=] W/m-K If k = constant: Magnitude of k: Metals: k  100 W/m-K Non-metals: k  1 - 10 W/m-K Liquids: k  0.1 - 10 W/m-K Gases: k  0.01 – 0.1 W/m-K Insulation: k  0.01 – 0.1 W/m-K Baratuci ChemE 260 April 11, 2005

Convection Heat Transfer Convection is the combination of conduction and fluid motion For the same fluid and conditions: Qconv > Qcond Forced Convection Fluid motion is driven by an external force, such as pressure Free or Natural Convection Fluid motion is driven by density differences and buoyant forces Tf TS Velocity Profile Temperature TS > Tf T = Tf Baratuci ChemE 260 April 11, 2005

Newton’s Law of Cooling Hot surface: Cold surface: h = convection heat transfer coefficient [=] W/m2-K Depends on fluid and surface properties Depends on the nature of the fluid velocity profile Magnitude of h: Free convection, gases: h  2 - 25 W/m2-K Free convection, liquids: h  50 - 1000 W/m2-K Forced convection, gases: h  25 - 250 W/m2-K Forced convection, liquids: h  50 – 20,000 W/m2-K Boiling phase change: h  2500 – 1x105 W/m2-K Remember that q = heat flux. Baratuci ChemE 260 April 11, 2005

Radiation Heat Transfer Atoms emit photons in the infrared part of the spectrum. The photons carry thermal energy to the surface that absorbs them.  = emissivity We usually assume  = 1 Radiation exchange between a body its surroundings If  = 1: Boldly assume  body =  surr =  : T must be expressed in Kelvins or Rankine (an absolute T-scale. Emissivity is a measure of the ability of a surface to emit thermal radiation s = Stefan-Boltzmann Constant = 5.67 x 10-8 W/m2-K4. Baratuci ChemE 260 April 11, 2005

Example #1 Air undergoes a three-process cycle. Find the net work done for 2 kg of air if the processes are: Process 1-2: constant pressure expansion Process 2-3: constant volume cooling Process 3-1: constant temperature compression Data: T1 = 100oC T2 = 600oC P1 = 200 kPa Answers: W12 = 287 kJ, W23 = 0 kJ, W31 = -182 kJ Wcycle = 105 kJ

Next Class 1st Law of Thermodynamics Problem Solving Proceedure Energy is neither created nor destroyed One of the 2 most important relationships in this course Problem Solving Proceedure A system to help avoid overlooking important aspects of a problem Saves time on unfamiliar problems Baratuci ChemE 260 April 11, 2005