ics day, ember 9, 2004 Ch 18: diagrams isobaric process isochoric process isothermal process adiabatic process 2nd Law of Thermodynamics Class Reviews/Evaluations For the rest of the semester day,. 9, 3-5pm and 7-9pm Monday,. 13, 2004 10:30 am 12:30 pm everything Hint: Be able to do the homework (graded AND recommended) and you ll do fine on the exam! I ll be available for questions, though. You may bring one 8.5 X11 crib sheet (handwritten on both sides), a pencil or pen, and a scientific calculator with you. I will put any constants and mathematical formulas that you might need on a single page attached to the back of the exam. Monday,. 13, 2004 10:30 am 12:30 pm everything Monday,. 13, 2004 10:30 am 12:30 pm everything art 1: Fluids & Thermodynamics 3 sections - you choose 2 7.5% of overall grade topics covered: heat transfer: radiation, conduction, convection calorimetry fluids - buoyancy art 2: Cumulative 5 sections - you chose 3 1 multiple choice section (required) 4 other sections, one of them essay - you choose 2 15% of overall grade topics covered: MC (everything), graphing, kinematics, Newton s Laws, work, energy, collisions, rotation, oscillations, thermodynamics 1
Due by 5 pm this Friday Online -- 45 min 5 C credit points No need to study for it It s really a test for the effectiveness of my teaching style this semester. Do your best, but no books, notes, help from others, etc. Follow the link on our class home page: http://physics.valpo.edu/courses/p Worksheet #1 Break up into 5 groups of ~ 4 students each. Each group will tackle on of the following scenarios, evaluating the W, Q, ΔK cm, ΔU cm, ΔE th, and for each system. 1: a steel block slides to rest as it moves up a rough, inclined surface 2: a rigid cylinder of an ideal gas is held still in a flame. 3: an expanding spring pushes a rigid cylinder of gas across a frictionless surface 4: an expanding spring pushes in a piston on a well-insulated cylinder of gas 5: a steel block is held at rest in a flame. First, a few simplifying assumptions: Use a - diagram. Quasi-static: the process occurs slowly enough that the system and its surroundings are always in thermal equilibrium. Reversibility: the system and its surroundings must return to exactly the same states in which they were before the process. rocesses involving friction are irreversible. lot the values of pressure and volume as energy is exchanged between the gas and its surrounding environment. Isobaric: Constant pressure processes Isobaric: Constant pressure processes In order for a gas to maintain a constant pressure while exchanging heat with its environment, the volume must change. W = Δ - diagrams: Isobaric The work done BY the system can be negative - for example, if the volume decreases. W = Δ - diagrams: Isobaric 2
Specific Heat at Constant ressure How much heat is added/removed from an ideal gas when the volume changes at constant pressure? Another tabulated property of the gas, the molar specific heat at constant pressure (C ) helps us to figure it out: Q = nc Isochoric: Constant volume processes Here, the pressure in the gas changes in response to the heat fluxes, but the gas does no work since the volume is constant. W = 0 - diagrams: Isochoric Isochoric: Constant volume processes From the 1st Law, we then know that the change in thermal energy of the system equals the heat flux into the system: Q = ΔE th - diagrams: Isochoric The - diagram below shows two processes, both of which start at the same pressure and volume and end at the same pressure and volume. How does the work done by the gas in process A compare to that done in process B? A B Worksheet #2 1) W A = W B = 0 2) W A = W B <> 0 3) W A > W B 4) W A < W B 5) Need more information Specific Heat at Constant olume How much heat is added/removed from an ideal gas when the pressure changes at constant volume? Internal Energy & C ΔE th = nc Another tabulated property of the gas, the molar specific heat at constant volume (C ) helps us to figure it out: Q = ΔE th = nc This important result is true, regardless of the process. A change in the internal or thermal energy of a gas is directly proportional to the change in temperature. The proportionality constant is the number of moles times the molar heat capacity at constant volume. 3
Specific Heat: C For a monatomic ideal gas, we can solve exactly. In an isochoric (constant volume) process, the work done by the system equals 0. So From kinetic theory we have Q = ΔE th ΔE th = 3 2 nr So, we get nc = 3 2 nr C = 3 2 R Specific Heat: C For a monatomic ideal gas, we can solve exactly. From the 1st Law of Thermodynamics: For isobaric processes: And for a monotomic, ideal gas, we know From the ideal gas law: Q W = ΔE th Q = nc ΔE th = 3 2 nr Δ = nr W = Δ Specific Heat: C For a monatomic ideal gas, we can solve exactly. Isothermal: Constant temperature processes utting this all together: nc nr = 3 2 nr Finally, we have C = 5 2 R From the ideal gas law: = Nk B T = constant So there s a direct relationship between and. - diagrams: Isothermal Isothermal: Constant temperature processes Using calculus, we find that the area under such curves, and hence, the work done by the system, is given by W = Nk B T ln f i - diagrams: Isothermal ressure (a) Isothermal: Constant temperature processes 2.50E+04 2.00E+04 1.50E+04 1.00E+04 5.00E+03 Increasing T 0.00E+00 0 1 2 3 olume (m 3 ) 300 K 500 K 700 K 900 K Note that the isotherms form a family of curves asymptotic to the and axes, with higher temperatures found as you move diagonally up and to the right. - diagrams: Isothermal 4
A cylinder contains 7.0 g of diatomic nitrogen gas. How much work does this gas do on its surroundings when it is compressed to half its original volume at a constant temperature of 80 0 C? Worksheet #3 Adiabatic: No heat flows into or out of the system Adiabatic curves have γ where γ = C C = = constant 5 R 2 3R 2 = 5 3 - diagrams: Adiabatic Adiabatic: No heat flows into or out of the system From the 1st law with Q = 0: W = ΔE th Entropy: A measure of the lack of order in a system High order (low entropy): Low order (high entropy): W = nc - diagrams: Adiabatic These systems aren t static either: if T > 0, the molecules are moving around as well. What happens when I bring these two systems into thermal contact with one another? High order (low entropy): Low order (high entropy): High order (low entropy): Low order (high entropy): 5
Warming What happens when I bring these two systems into thermal contact with one another? Equal Order - Same Temperature Cooling Entropy of an isolated system never decreases. Entropy will always remain the same (best case scenario for systems in thermal equilibrium with their surroundings) or increase until they reach thermal equilibrium. In order to increase the order of a system, you need to do work on the system. (Think of cleaning your room.) The universe tends toward less order with time. So, it s quite natural that your room gets dirty. Statement from your text: Heat is always transferred from the hot system to the cold system when they come into thermal contact. You made it! Good luck with your studying and in all of your s. Remember to get a good night s sleep. Have a very Merry Christmas and a Happy New Year! lease fill out all of the evaluation materials. You will receive 5 C points each. Department form ics class form I appreciate your time and comments and will read them over before the start of ics 112 in the spring. 6