Physics Notes - week of 4.11.16
Physics Notes - week of 4.11.16 PHYS2001
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This 9 page Class Notes was uploaded by Grace Lillie on Saturday April 16, 2016. The Class Notes belongs to PHYS2001 at University of Cincinnati taught by Alexandru Maries in Fall 2016. Since its upload, it has received 10 views. For similar materials see College Physics 1 (Calculus-based) in Physics 2 at University of Cincinnati.
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Date Created: 04/16/16
Chapter 22 – Heat Engines, Entropy, and the Second Law of Thermodynamics 22.1 – Heat Engines and the Second Law of Thermodynamics - heat engine—a device that takes in energy by heat and expels a fraction of that energy by work E.g. coal is burned to heat water to steam to turn a turbine to drive a generator The cyclic process of a heat engine involves: 1. the working substance absorbs energy from a high-temperature energy reservoir 2. work is done by the engine 3. energy is expelled by heat to a lower-temperature reservoir *when doing the math, absolute values make all energy transfers by heat positive. Use signs intentionally to indicate direction* W eng | h¿Q ∨c net work done by a heat engine - thermal efficiency—of a heat engine. The ratio of net work done by the heat engine during one cycle to the energy input at the higher temperature during the cycle (the ratio of what you gain to what you give: W eng | h | |c | |c e= = =1− | |h | h | |h -Kelvin-Planck form of the second law of thermodynamics—It’s impossible to make a heat engine that produces no effect other than the input of energy by heat from a reservoir and the performance of an equal amount of work in a cyclic process. (in other words, heat engines can’t be perfectly efficient) 22.2 – Heat Pumps and Refrigerators - the natural direction of energy transfer by heat is from hot to cold - you need to put energy (by work) into a device to transfer energy from the cold to the hot reservoir - heat pumps and refrigerators do this - Clausius statement—It’s impossible to make a cyclic machine that transfers energy continuously by heat from one object to another object at a higher temperature without inputting energy by work. (energy can’t transfer by heat from cold to hot without work) - coefficient of performance—of a heat pump. Similar to thermal efficiency (gain/lose): energytransferred atlowtemperature| c COP (oolingmode ) = workdoneonheat pump W | | COP (eatingmode ) energytransferred at hightemperat=re c workdoneonheat pump W 22. 3 – Reversible and Irreversible Processes - reversible process—the system can be returned to initial conditions along the same path on a PV diagram, and every point along the path is an equilibrium state - irreversible process aren’t reversible. *All natural processes* - some processes are almost reversible: if it occurs very slowly so that the system is always nearly in an equilibrium state, the process can be approximated as being reversible. But for it to be truly reversible, no nonconservative effects that transform mechanical to internal energy can be present (turbulence, friction, etc.) 22.4 – The Carnot Engine - Carnot engine—*theoretical* show that a heat engine in an ideal, reversible cycle (Carnot cycle) is the most efficient engine possible and can establish an upper limit on the efficiency of all other engines. - Carnot’s theorem—No real heat engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs. - the efficiency of a Carnot engine depends only on the temperatures of the reservoirs - the Carnot cycle has four processes: 1. isothermal expansion: the gas absorbs energy from the hot reservoir and does work to raise the piston. 2. adiabatic expansion: the hot reservoir is replaced by a thermally nonconducting wall so no heat enters or leaves the system. Temperature decreases and the gas does work to raise the piston. 3. isothermal compression: a cold reservoir replaces the nonconducting wall and the gas expels energy to the reservoir and the piston does work on the gas. 4. adiabatic compression: a nonconducting wall replaces the cold reservoir and the temperature of the gas increases and the piston does work on the gas. T e =1− c C T efficiency of a Carnot engine. Efficiency is on 100% if T =0 Kcwhich h doesn’t happen. It’s usually near room temperature, so efficiency is increased by raising T h Th Tc COP hCa(ingmode = ) CO P C(oling mode = ) T hT c T hT c 22.5 – Gasoline and Diesel Engines - 6 processes occur in each cycle of a gasoline engine (p.665-666): a. piston moves down and air/fuel drawn into cylinder which provides the energy input. Volume increases V to V 2 1 b. piston moves up, air-fuel mixture compressed adiabatically to V and 2 temperature increases from T to T A WorkBdone on gas is positive, negative the area under the curve AB. c. spark plug fires quickly while piston at highest position. Energy transforms from potential energy stored in chemical bonds in the fuel to internal energy related to temperature. Pressure and temperature increase T to T whileB C volume remains constant, so no work done. d. gas expands adiabatically V to V2, tem1erature drops T to T . WoCk is D done by the gas in pushing the piston down, the area under the curve CD. e. occurs when exhaust valve opened. Pressure drops, piston almost stationary, volume about constant. Energy expelled from the interior of the cylinder. f. piston moves up while exhaust valve open. Energy still expelled, volume decreases V 1o V ,2and the cycle repeats. This process is represented by the Otto cycle (see PV diagram above). If the air- e=1− 1 fuel mixture is an ideal gas, efficiency is: (V /V )γ−1 1 2 - V /V is the compression ratio. Efficiency increases as this increase 1 2 - γ is the ratio of molar specific heatsPC VC - actual efficiency less than theoretical because of friction, energy transfer by conduction through cylinder walls, incomplete combustion, etc. - diesel engines are similar but no spark plug and the compression ratio is much greater so the combustion temperature is higher 22.6 – Entropy - Temperature and internal energy are state variables (depend on current state, not process) - entropy is a state variable and an ABSTRACT concept - microstate—configuration of the individual constituents of the system - macrostate—description of the system’s conditions from a macroscopic point of view. - uncertainty, choice, and probability: if one is high, the others are high, and vice versa - entropy—(S) represents the level of uncertainty, choice, probability, or missing information in a system V S=k BnW=nRln (V) how to evaluate entropy numerically for a thermodynamic m system - B is Boltzmann’s constant - W is the number of microstates associated with the macrostate - V is macroscopic volume, V im microscopic volume of a single molecule *the second equation addresses spatial portion of entropy, but there is also a temperature-dependent portion of entropy - as temperature increases, there is more uncertainty so higher entropy 22.7 – Changes in Entropy for Thermodynamic Systems - Thermodynamic systems change continuously between microstates. In equilibrium, there is one macrostate but the system still fluctuates between microstates. - if a system starts in a low-probability macrostate, it will naturally progress to a higher-probability macrostate. Spontaneous increases in entropy are natural. - change in entropy is related to energy spreading dS= dQ r T change in entropy for an infinitesimal process. rQ is the amount of energy transferred by heat when the system follows a reversible path between states. The subscript r means its reversible. dQ rs positive when energy is absorbed and negative when energy is expelled. f fdQ r ∆ S=∫dS= ∫ Change in entropy for a finite process. *path doesn’t matter* i i T ∆ S=k ln W f B (W) i - the total change in entropy for a Carnot engine operating in a cycle is ZERO: ∆ S=0 - for any reversible cycle, change in entropy is ZERO V f ∆ S=nRln (V) entropy change for a gas in adiabatic free expansion. Entropy i increases. ∆ S= Q +Q =Q 1− 1 >0 T c Th (Tc T h) change in entropy for thermal conduction (increases) 22.8 – Entropy and the Second Law Entropy statement of the second law of thermodynamics: The entropy of the Universe increases ni all real processes
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