PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 19 Last Lecture First Law of Thermodynamics Q U W by the gas Work done by on a gas W by the gas P V W on the gas Some Vocabulary P Isobaric V P constant Isovolumetric P V constant W 0 Isothermal T constant U 0 ideal gas V P V Adiabatic Q 0 P V P V Diagrams P Path moves to right Wby P the gas Area under curve V Path moves to left Wby the gas Area under curve V Won the gas Wby the gas Work from closed cycles Clockwise cycle WA B A Area Counterclockwise cycle WA B A Area U 0in closed cycles work done by gas Example 12 8a Consider an ideal gas undergoing the trajectory through the PV diagram In going from A to B to C the work done BY the gas is 0 a b c C P B A V Example 12 8b In going from A to B to C the change of the internal energy of the gas is 0 C P B A V a b c Example 12 8c In going from A to B to C the amount of heat added to the gas is 0 C D P B A V a b c Example 12 8d In going from A to B to C to D to A the work done BY the gas is 0 C D P B A V a b c Example 12 8e In going from A to B to C to D to A the change of the internal energy of the gas is 0 C D P B A V a b c Example 12 8f In going from A to B to C to D to A the heat added to the gas is 0 C D P B A V a b c Consider a monotonic ideal gas a What work was done by 75 20 000 J the gas from A to B Example 12 7 P kPa A b What heat was added to50 J the gas between 20 000 A and B c What work was done by 25 10 000 J the gas from B to C d What heat was added to the gas between 25 000 B and C J e What work was done by 0 A the gas from C to f What heat was added to 15 000 J the gas from C to A B C 0 2 V m3 0 4 0 6 Example 12 7 Continued g What was total work done by gas in cycle P kPa Qin A WAB WBC WCA 10 000 J h What was total heat added to gas in cycle B C QAB QBC QCA 10 000 J This does NOT mean that the engine is 100 efficient Qin QAB QCA 35 000 J Qout QBC 25 000 J V m3 Qout Exhaust Weng Qin Qout Heat Engines Described by a cycle with Qhot Qhot heat that flows into engine from source at Thot Qcold heat exhausted from engine at lower temperature Tcold W work done by engine engine W Qcold Efficiency is defined engine Qhot Qcold W Qcold e 1 Qhot Qhot Qhot using W Qhot Qcold 2nd Law of Thermodynamics version 1 No heat engine can be 100 efficient The most efficient engine is the Carnot Engine an idealized engine for which Qcold Tcold Qhot Thot eCarnot W Qcold Tcold 1 1 Qhot Qhot Thot T in Kelvin e eCarnot In practice we always have Carnot Cycle Example 12 9 An ideal engine Carnot is rated at 50 efficiency when it is able to exhaust heat at a temperature of 20 C If the exhaust temperature is lowered to 30 C what is the new efficiency e 0 585 Refrigerators Just a heat engine run in reverse Pull Qcold from fridge Exhaust Qhot to outside Coefficient of Performance Qcold COP cooling W Qhot fridge Qcold st efficient is Carnot refrigerator COP cooling COPCarnot W Tcold Thot Tcold Note Highest COP for small T differences Heat Pumps Same as refrigerator except Pull Qcold from environment Exhaust Qhot to inside of house Coefficient of Performance Qhot COP heating W Qhot heat pump W Qcold gain most efficient is Carnot COP heat COPCarnot Thot Thot Tcold ike Refrigerator Best performance for small T Example 12 10 A modern gas furnace can work at practically 100 efficiency i e 100 of the heat from burning the gas is converted into heat for the home Assume that a heat pump works at 50 of the efficiency of an ideal heat pump If electricity costs 3 times as much per kw hr as gas for what range of outside temperatures is it advantageous to use a heat pump Assume Tinside 295 K 5 T 295 245 8 K 27 C 6 Entropy Measure of Disorder of the system randomness ignorance S kBlog N N of possible arrangements for fixed E and Q 1000 900 800 700 600 500 400 300 200 100 0 0 12 1 11 2 10 3 9 4 8 5 7 6 6 7 5 8 4 9 3 10 2 11 1 12 0 Relative probabilities for 12 molecules to arrange on two halves of container 2nd Law of Thermodynamics version 2 The Total Entropy of the Universe can never decrease On a macroscopic level one finds that adding heat raises entropy S Q T Defines temperature in Kelvin Why does Q flow from hot to cold Consider two systems one with TA and one with TB Allow Q 0 to flow from TA to TB Entropy changes by S Q TB Q TA This can only occur if S 0 requiring TA TB System will achieve more randomness by exchanging heat until TB TA Carnot Engine Carnot cycle is most efficient possible because the total entropy change is zero It is a reversible process For real engines S Senvironment Qcold Qhot 0 Tcold Thot W Qcold Tcold e 1 1 eCarnot Qhot Qhot Thot Example 12 11a An engine does an amount of work W and exhausts heat at a temperature of 50 degrees C The chemical energy contained in the fuel must be greater than and not equal to W a True b False Example 12 11b A locomotive is powered by a large engine that exhausts heat into a large heat exchanger that stays close to the temperature of the atmosphere The engine should be more efficient on a very cold day than on a warm day a True b False Example 12 11c An air conditioner uses an amount of electrical energy U to cool a home The amount of heat removed from the home must be less than or equal to U a True b False Example 12 11d A heat pump uses an amount of electrical energy U to heat a home The amount of heat added to a home must be less than or equal to U a True b False
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