Work done by a gas Lecture 23 Announcements 1 Exam starts Thursday a Thursday will be the in class exam review i No warmup quiz b Thursday evening will be the TA exam review 7 9 pm C215 Eyring 2 Exam ends on Tuesday not Wednesday a Testing Center not open on Wed due to Thanksgiving 3 Homework 19 due tomorrow a Next homework not due until Dec 3 Two weeks off 4 No class a week from today Friday classes meet 1 m3 of an ideal gas at 300 K supports a weight in a piston such that the pressure in the gas is 200 000 Pa about 2 atm The gas is heated up It expands to 3 m3 How much work did the gas do as it expanded Result 5th edition Wby gas P V for constant P Wby gas 0 when Work done on a gas 6th 7th 8th editions Won gas P V for constant P Colton Lecture 23 11 18 08 pg 1 Internal energy of an ideal gas U Colton Lecture 23 11 18 08 pg 2 P V diagrams Return to Equipartition Theorem The total kinetic energy of a system is shared equally among all of its independent parts on the average once the system has reached thermal equilibrium a change in state Monatomic ideal gas only kinetic energy possible 3 directions average KE molecule 3 2 kBT total KE N 3 2 kBT U 3 2 NkBT 3 2 nRT State postulate any two independent variables determine the state P V T U etc P Each degree of freedom of each molecule has an energy of kBT independent parts larger for molecules that can rotate vibrate requires more than one atom such molecules have more internal energy Won gas 0 when V Work done area under curve but careful with sign How to tell at a glance if the temperature has increased or decreased Isothermal curves contours of constant T P monoatomic Other substances U is more complicated depends on temperature Diatomic around 300K U 5 2 nRT 2 rotational directions that take energy Colton Lecture 23 11 18 08 pg 3 V U for an isothermal process is because What is U for the constant P process at top of page Colton Lecture 23 11 18 08 pg 4 1st Law of Thermodynamics P V diagram examples Isothermal process U Qadded Won system note 5th edition uses Wby system P System the object you are studying Environment what it interacts with V What does it mean Use 5th edition version U Qadded Wby system Qadded U Wby system Meaning of 1st Law Heat added can go either towards increasing internal energy temperature or doing work by the gas U Won gas Q Another process P Final warning Be careful with all the signs U is positive if Qadded is positive if V Won system is positive if U Won gas Colton Lecture 23 11 18 08 pg 5 A gas in a piston expands from point A to point B on the P V plot via either path 1 or path 2 Path 2 is a combo path going down first then over A P 1 2 B V Clicker quiz 1 The gas does the most work in a path 1 b path 2 c neither it s the same Q Colton Lecture 23 11 18 08 pg 6 Adiabatic expansion or compression Adiabatic no heat added either because system is insulated or V is fast so no time for much heat to go in out of gas Q W U Adiabatic curves are steeper than isothermal curves P Clicker quiz 2 In process 1 the work done a puts energy into the system b takes energy out of the system c has no effect on the energy of the system Clicker quiz 3 The process in which U is the greatest magnitude is a path 1 b path 2 c neither it s the same How much work is done in first half of path 2 What is this path physically Colton Lecture 23 11 18 08 pg 7 V No heat added does not mean no temperature change Demos adiabatic compression and cotton freezing by expansion Ralph question how does isothermal compression work Colton Lecture 23 11 18 08 pg 8 Two situations Clicker quiz You compress air very quickly in an engine cylinder Determine the signs of Q W and U Won gas U a Qadded Won gas U b Qadded 0 Won gas U c Qadded Won gas 0 U d Qadded Won gas U 0 e Qadded Clicker quiz You heat a spray can in a fire and volume stays about the same it doesn t explode System gas in the can Determine the signs of Q W and U a Qadded Won gas U Won gas U b Qadded 0 Won gas U c Qadded d Qadded Won gas 0 U Won gas U 0 e Qadded Cyclical Processes P State 1 V U Won gas Q Engines The basic idea energy transformation work heat engine exhaust Notation Qh Qc Th Tc Wnet Efficiency how good is your engine at converting heat to work Definition e Engine Power work per time as usual Colton Lecture 23 11 18 08 pg 9 Colton Lecture 23 11 18 08 pg 10 Demo Thermoelectric converter engine Real engines modeled by PV diagram cycles Worked Problem An engine produces power of 5000 W at 20 cycles second Its efficiency is 20 What are Wnet Qh and Qc per cycle Example Gasoline engines Piston is compressed quickly Heat is then added quickly by igniting fuel Piston then expands quickly Heat is then expelled quickly by getting rid of old air Same air is not re used the cycle is just an approximation The Otto cycle What do those quantities represent Image credit http www grc nasa gov WWW K 12 airplane otto html Answers 250 J 1250 J 1000 J Colton Lecture 23 11 18 08 pg 11 Colton Lecture 23 11 18 08 pg 12 2nd Law of thermodynamics Carnot s Theorem You can t even convert most of the heat into work Heat spontaneously flows from hot to cold not the other way around Why Order From textbook which hand is more likely emax eC 1 Tc Th C for Carnot Organized Energy lost by irreversibilities Irreversibilities occur when heat is added during a temperature change Most efficient engine possible Carnot engine all heat added during constant temperature processes but which is more likely a straight flush or a garbage hand Boltzman 3D program revisited increasing entropy P Another version of the law In an engine you can t convert all the heat into usable work V How much power Isothermal slow typically Why are they equivalent Colton Lecture 23 11 18 08 pg 13 A B P C V Clicker quiz 1 The process that does the most work magnitude is Clicker quiz 2 The process that is at constant temperature is Clicker quiz 3 The process that leaves the system at the highest T is Clicker quiz 4 The process in which the magnitudes …