PHYSICS 231 Lecture 25 Heat Heat exchange PHY 231 1 Boyle Charles Gay Lussac IDEAL GAS LAW PV T nR n number of particles in the gas mol R universal gas constant 8 31 J mol K If no molecules are extracted from or added to a system PV constant T P1V1 P2V2 T1 T2 PHY 231 2 2 1 2 PV N mv Microscopic 3 2 Macroscopic PV Nk B T 2 1 2 T mv 3k B 2 Temperature average molecular kinetic energy 1 2 3 mv k B T Average molecular kinetic energy 2 2 3 3 E kin Nk B T nRT Total kinetic energy 2 2 3k b T 3RT rms speed of a molecule 2 v rms v M Molar mass kg mol m M PHY 231 3 Internal energy In chapter 10 The internal total energy for an ideal gas is the total kinetic energy of the atoms particles in a gas For a non ideal gas the internal energy is due to kinetic and potential energy associated with translational motion rotational motion vibrational motion intermolecular potential energy PEideal gas 0 PEnon ideal gas PEliquid PEsolid PE PE negative PHY 231 R 5 Heat Heat The transfer of energy between objects because their temperatures are different Heat energy transfer Symbol Q Units Calorie cal or Joule J 1 cal 4 186 J energy needed to raise 1g of water by 10C PHY 231 6 Heat transfer to an object The amount of energy transfer Q to an object with mass m when its temperature is raised by T Q cm T Change in temperature Energy transfer J or cal Mass of object Specific heat J kgoC or cal goC PHY 231 7 Example A 1 kg block of Copper is raised in temperature by 10oC What was the heat transfer Q Answer Q cm T 387 1 10 3870 J 1 cal 4 186 J Q 924 5 cal PHY 231 8 Another one A block of Copper is dropped from a height of 10 m Assuming that all the potential energy is transferred into internal energy heat when it hits the ground what is the raise in temperature of the block ccopper 387 J kgoC Potential energy mgh 10mg J All transferred into heat Q Q cm T 10mg 387m T T 10g 387 0 25oC PHY 231 9 Calorimetry If we connect two objects with different temperature energy will transferred from the hotter to the cooler one until their temperatures are the same If the system is isolated Qcold Qhot mcoldccold Tfinal Tcold mhotchot Tfinal Thot the final temperature is Tfinal PHY 231 mcoldccoldTcold mhotchotThot mcoldccold mhotchot 10 Demo heating water with a ball of Lead A ball of Lead at T 100oC with mass 300 g is dropped in a glass of water 0 3 L at T 200C What is the final after thermal equilibrium has occurred temperature of the system cwater 1 cal goC clead 0 03 cal goC water 103kg m3 Qcold Qhot mwatercwater Tfinal Twater mleadclead Tfinal Tlead mwatercwaterTwater mleadcleadTlead Tfinal mwatercwater mleadclead 0 3 1 20 0 3 0 03 100 0 3 1 0 3 0 03 6 9 0 309 22 3oC PHY 231 11 An example The contents of a can of soda 0 33 kg which is cooled to 4oC is poured into a glass 0 1 kg that is at room temperature 200C What will the temperature of the filled glass be after it has reached full equilibrium glass and liquid have the same temperature Given cwater 4186 J kgoC and cglass 837 J kg0C Qcold Qhot mwatercwater Tfinal Twater mglasscglass Tfinal Tglass mwatercwaterTwater mglasscglassTglass Tfinal mwatercwater mglasscglass 0 33 4186 4 0 1 837 20 0 33 4186 0 1 837 4 9oC PHY 231 12 And another A block of unknown substance with a mass of 8 kg initially at T 280K is thermally connect to a block of copper 5 kg that is at T 320 K ccopper 0 093 cal g0C After the system has reached thermal equilibrium the temperature T equals 290K What is the specific heat of the unknown material in cal goC Qcold Qhot munknowncunknown Tfinal Tunknown mcopperccopper Tfinal Tcopper cunknown mcopperccopper Tfinal Tcopper munknown Tfinal Tunknown cunkown 5000 0 093 290 320 0 17 cal goC 8000 290 280 PHY 231 copper 13 Phase Change GAS high T Q csolidm T Solid low T Q cgasm T Gas liquid liquid medium T liquid solid Q cliquidm T PHY 231 14 Gas liquid Phase change When heat is added to a liquid potential energy goes to 0 the energy stored in the stickiness of the liquid is taken away DURING THE CHANGE FROM LIQUID TO GAS THE KINETIC ENERGY DOES NOT CHANGE AND SO THE TEMPERATURE DOES NOT CHANGE ALL ADDED HEAT GOES TO CHANGING PE When heat is taken from a gas potential energy goes to the stickiness of the fluid DURING THE CHANGE FROM GAS TO LIQUID THE KINETIC ENERGY DOES NOT CHANGE AND SO THE TEMPERATURE DOES NOT CHANGE ALL REMOVED HEAT GOES TO CHANGING PE PHY 231 15 liquid Phase change solid When heat is added to a solid to make a liquid potential energy in the bonds between the atoms become less DURING THE CHANGE FROM SOLID TO LIQUID THE KINETIC ENERGY DOES NOT CHANGE AND SO THE TEMPERATURE DOES NOT CHANGE ALL ADDED HEAT GOES TO CHANGING PE When heat is taken from a liquid the bonds between atoms becomes stronger potential energy is more negative DURING THE CHANGE FROM LIQUID TO SOLID THE KINETIC ENERGY DOES NOT CHANGE AND SO THE TEMPERATURE DOES NOT CHANGE ALL REMOVED HEAT GOES TO CHANGING PE PHY 231 16 Okay the Temperature does not change in a phase transition But what is the amount of heat added to make the phase transition Gas liquid Qgas liquid MLv Qliquid gas MLv M mass Lv latent heat of vaporization J kg or cal g depends on material Use the table 11 2 in the book for LON CAPA PHY 231 17 solid liquid Qliquid solid MLf Qsolid liquid MLf M mass Lf latent heat of fusion J kg or cal g depends on material Use the table 11 2 in the book for LON CAPA PHY 231 18 Phase Change GAS high T Gas liquid Q mLv Q csolidm T Solid low T Q cgasm T liquid medium T Q cliquidm T PHY 231 liquid solid Q mLf 19 PHY 231 20 A Ice from 30 to 0oC B Ice to water C water from 0oC to 100oC D water to steam E steam from 100oC to 1500C TOTAL Ice with T 30oC is heated to steam of T 1500C How many heat in cal has been added in total cice 0 5 cal goC cwater 1 0 cal goC csteam 0 480 cal goC Lf 540 cal g Lv 79 7 cal g m 1 kg 1000g Q 1000 0 5 30 15000 cal Q 1000 540 540000 cal Q 1000 1 0 100 100000 cal Q 1000 79 7 79700 cal Q 1000 0 48 50 24000 cal Q 758700 …
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