PHY PHYSICS 231 Lecture 27: Heat & Heat exchange Remco Zegers Walk-in hour:Monday 9:15-10:15 Helproom

PHY 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:

PHY Microscopic Macroscopic Temperature ~ average molecular kinetic energy Average molecular kinetic energy Total kinetic energy rms speed of a molecule M=Molar mass (kg/mol)

PHY quiz (extra credit) A gas is kept at a pressure P and temperature T in a volume V. The temperature is increased by a factor of 5, while the gas is allowed to expand to a volume that is 10 times larger than the original volume. What is the new value of the pressure, relative to the old value (P new /P old )? a)0.1 b)0.2 c)0.5 d)2 e)5

PHY 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 |PE ideal gas =0| < |PE non-ideal gas | < |PE liquid | < |PE solid | PE R PE: negative!

PHY 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 = J (energy needed to raise 1g of water by 1 0 C)

PHY Heat transfer to an object Q=cmTQ=cmT Energy transfer (J or cal) Specific heat (J/(kg o C) or cal/(g o C) Mass of object Change in temperature The amount of energy transfer Q to an object with mass m when its temperature is raised by  T:

PHY Example A 1 kg block of Copper is raised in temperature by 10 o C. What was the heat transfer Q.?

PHY 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 (c copper =387 J/(kg o C))?

PHY 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: Q cold =-Q hot m cold c cold (T final -T cold )=-m hot c hot (T final -T hot ) the final temperature is: T final = m cold c cold T cold +m hot c hot T hot m cold c cold +m hot c hot

PHY An example The contents of a can of soda (0.33 kg) which is cooled to 4 o C is poured into a glass (0.1 kg) that is at room temperature (20 0 C). What will the temperature of the filled glass be after it has reached full equilibrium (glass and liquid have the same temperature)? Given c water =4186 J/(kg o C) and c glass =837 J/(kg 0 C)

PHY 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 (c copper =0.093 cal/g 0 C). After the system has reached thermal equilibrium the temperature T equals 290K. What is the specific heat of the unknown material in cal/g o C? ???? copper

PHY Demo: heating water with a ball of Lead A ball of Lead at T=100 o C with mass 300 g is dropped in a glass of water (0.3 L) at T=20 0 C. What is the final (after thermal equilibrium has occurred) temperature of the system? (c water =1 cal/g o C, c lead =0.03 cal/g o C  water =10 3 kg/m 3 ) T final = = (0.3*1*20+0.3*0.03*100)/(0.3*1+0.3*0.03)= = 6.9/0.309=22.3 o C Q cold =-Q hot m water c water (T final -T water )=-m lead c lead (T final -T lead ) m water c water T water +m lead c lead T lead m water c water +m lead c lead

PHY Phase Change GAS(high T) liquid (medium T) Solid (low T) Q=c gas m  T Q=c liquid m  T Q=c solid m  T Gas  liquid liquid  solid

PHY Phase change Gas  liquid 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 Phase change liquid  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 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 Q gas  liquid =-ML v Q liquid  gas =+ML v L v =latent heat of vaporization (J/kg or cal/g) depends on material. Use the table 11.2 in the book for LON-CAPA M:mass

PHY solid  liquid Q liquid  solid =-ML f Q solid  liquid =+ML f L f =latent heat of fusion (J/kg or cal/g) depends on material. M:mass Use the table 11.2 in the book for LON-CAPA

PHY Phase Change GAS(high T) liquid (medium T) Solid (low T) Q=c gas m  T Q=c liquid m  T Q=c solid m  T Gas  liquid liquid  solid Q=mL f Q=mL v

PHY

PHY Ice with T=-30 o C is heated to steam of T=150 0 C. How many heat (in cal) has been added in total? c ice =0.5 cal/g o C c water =1.0 cal/g o C c steam =0.480 cal/g o C L f =540 cal/g L v =79.7 cal/g m=1 kg=1000g

PHY For next lecture’s quiz: bring calculator!