UH PHYS 1302 - Ch18 (13 pages)

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Ch18



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Ch18

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ch 18 study guide


Pages:
13
School:
University of Houston
Course:
Phys 1302 - Introductory to Physics II
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Chapter 18 The Laws of Thermodynamics 1 The Zeroth Law of Thermodynamics If object A is in thermal equilibrium with object C and object B is separately in thermal equilibrium with object C then objects A and B will be in thermal equilibrium Objects are in thermal equilibrium when they have the same temperature 2 The First Law of Thermodynamics The change in a system s internal energy U Uf Ui is related to the heat Q and the work W as follows U Q W 1 The first law is just conservation of energy specifically including heat Sign conventions Q 0 for heat gained by the system Q 0 for heat lost by the system W 0 for work done by the system W 0 for work done on the system Problem 18 3 A swimmer does 6 7 105 J of work and gives off 4 1 105 J of heat during a workout Determined U W and Q for the swimmer L Whitehead 1 Phys 1302 The work is done by the swimmer so W 6 7 105 J The heat is lost by the swimmer so Q 4 1 105 J U Q W 4 1 105 6 7 105 10 8 105 J The state of a system is determined by the temperature pressure and volume 3 Thermal Processes All of the processes that we re going to talk about are assumed to be quasi static reversible which means they occur so slowly that at any given time the system and its surroundings are in equilibrium We also assume there are no dissipative forces in the system Another way of saying it is that these processes are all reversible For a process to be reversible it must be possible to return both the system and its surroundings to exactly the same states they were in before the process began Friction is an example of an irreversible process Constant Pressure Process Suppose we have gas held in a cylinder with cross sectional area A The pressure is held constant at P0 but the volume of the gas expands moving the piston from position xi to position xf the gas is doing work on the piston The initial volume of the gas is Vi Axi and the final volume of the gas is Vf Axf The force the L Whitehead 2 Phys 1302 gas exerts on the piston is F P0 A so the work done by the gas is W F xf xi P0 A xf xi P0 Vf Vi In general for a constant pressure process that changes the volume V the work done by the gas is W P V 2 In the pressure vs volume plot above the area under the curve is P0 Vf Vi which is equal to the work done by the gas This applies to any process the work done by an expanding gas is equal to the area under the pressure vs volume curve representing the process Constant Volume Process Suppose we have a gas held in a container of fixed volume Suppose we add heat causing the pressure to increase Since the container has a fixed volume the gas does no work W 0 3 U Q W Q 4 Notice that the area under the pressure vs volume curve is zero as expected for zero work done Isothermal Process Constant Temperature L Whitehead 3 Phys 1302 For an ideal gas at constant temperature P V N kT constant so P is inversely proportional to V P constant V The work done by an expanding gas is equal to the area under the pressure vs volume curve For an isotherm curve the area under the curve is W N kT ln Vf Vf nRT ln Vi Vi 5 Calculus derivation don t show in class Z W F dx Z F dx Z P Adx Z P dV Z N kT dV V Z Vf dV N kT V Vi N kT ln Vf ln Vi Vf N kT ln Vi L Whitehead 4 Phys 1302 Adiabatic Process An adiabatic process is one in which no heat flows in or out of the system Q 0 6 U Q W W 7 Suppose we have a well insulated cylinder that does not allow heat flow in or out When the piston is pushed down the volume of the gas decreases but the temperature and pressure both increase When the volume is allowed to expand the pressure and temperature both decrease An adiabatic process can occur if the system is thermally insulated An adiabatic process can also occur when the process happens so rapidly that there is no time for heat to flow Problem 18 24 During an adiabatic process the temperature of 3 92 moles of a monatomic idea gas drops from 485 C to 205 C For this gas find a the work it does b the heat it exchanges with its surroundings and c the change in its internal energy Because its an adiabatic process the heat exchange is Q 0 The internal energy of an ideal gas is given by U 3 2 nRT The change in L Whitehead 5 Phys 1302 temperature is T Tf Ti 205 485 280K U W W U W Uf Ui 3 W nR Tf Ti 2 3 W 3 92moles 8 31J mole K 280K 2 W 1 37 104 J U W 1 37 104 J 4 Specific Heats for an Ideal Gas Constant Pressure Constant Volume skipping 5 The Second Law of Thermodynamics When objects of different temperatures are brought into thermal contact the spontanous flow of heat that results is always from the high temperature object to the low temperature object Spontaneous heat flow never proceeds in the reverse direction The second law is sometimes referred to as the arrow of time If you saw a video of a water droplet on someone s hand spontaneously turning into a snowflake and drifting upwards you would know the video is running backward That process could not happen spontaneously L Whitehead 6 Phys 1302 6 Heat Engines and the Carnot Cycle A heat engine is a device that converts heat into work In a steam engine heat is supplied to vaporize water in the boiler The steam enters the engine and expands moving a piston The movement of the piston supplies mechanical work to the external world The steam then goes into a condenser where it gives off heat and condenses to liquid form In a general heat engine heat is supplied by a hot reservoir the boiler in the steam engine Some of that heat is converted to work and the rest is given off as waste heat to the cold reservoir the condenser in the steam engine If Qh is the magnitude of the heat supplied by the hot reservoir and Qc is the magnitude of the heat given to the cold reservoir conservation of energy indicates that the work W done is W Qh Qc 8 The efficiency of the engine is defined as the fraction of the supplied heat that is converted to work Qh Qc Qc W 1 9 e Qh …


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