Lecture 24Purdue University, Physics 2201 Lecture 24 Heat PHYSICS 220

Lecture 24Purdue University, Physics 2202 Internal Energy Energy of all molecules including –Translational and rotational kinetic energy of molecules due to their individual random motions. –Vibrational energy (both kinetic and potential) of molecules and of atoms within molecules due to random vibrations about their equilibrium points. –Potential energy due to interactions between the atoms and molecules of the systems. –Chemical and nuclear energy (kinetic and potential energy associated with the binding of atoms to form molecules, the binding of electrons to nuclei to form atoms, and the binding of protons and neutrons to form nuclei). DOES NOT INCLUDE –Macroscopic motion of object –Potential energy due to interactions with other objects

Lecture 24Purdue University, Physics 2203 Heat Definition: Flow of energy between two objects due to difference in temperature –Note: similar to WORK –Object does not “have” heat (it has energy) Units: calorie –Amount of heat needed to raise 1g of water 1ºC –1 Calorie = 1 kcal = 1000 cal = 4186 Joules Heat flows from a system at higher temperature to one at lower temperature

Lecture 24Purdue University, Physics 2204 Heat Capacity and Specific Heat Heat capacity =Q/  T shows how much heat is required to change the T of object (system) Specific heat c= Q/m  T Q = c m  T Heat required to increase temperature depends on amount of material (m) and type of material Heat adds energy to object/system IF there is no dissipation then: Heat increases internal energy: Q =  U Heat increases temperature: Q = C  T

Lecture 24Purdue University, Physics 2205 Exercise After a grueling work out, you drink a liter of cold water (0 C). How many Calories does it take for your body to raise the water up to body temperature of 36 C? A) 36 B) 360 C) 3,600 D) 36,000 1 liter = 1,000 grams of H g x 1 calorie/(gram degree) x (36 degree) = 36,000 calories 36,000 calories = 36 Calories!

Lecture 24Purdue University, Physics 2206 Question Suppose you have equal masses of aluminum and copper at the same initial temperature. You add 1000 J of heat to each of them. Which one ends up at the higher final temperature A) aluminum B) copper C) the same  T = Q/cm Substance c in J/(kg-C) aluminum900 copper387 iron452 lead128 human body 3500 water 4186 ice 2000

Lecture 24Purdue University, Physics 2207 Two insulated buckets contain the same amount of water at room temperature. Two blocks of metal of the same mass, both at the same temperature, are warmer than the water in the buckets. One block is made of aluminum (c=0.9) and one is made of copper. You put the aluminum block into one bucket of water, and the copper (c=0.385) block into the other. After waiting a while you measure the temperature of the water in both buckets. Which is warmer? A) The water in the bucket containing the aluminum block B) The water in the bucket containing the copper block C) The water in both buckets will be at the same temperature iClicker Since aluminum has a higher specific heat than copper, you are adding more heat to the water when you dump the aluminum in the bucket (Q=mc  T).

Lecture 24Purdue University, Physics 2208 Specific Heat for Ideal Gas Monatomic Gas (single atom) Translational kinetic energy only At constant Volume work = 0 Q =  U = 3/2 nR  T C V = 3/2 R = 12.5 J/(K mole) Cv – specific heat at constant volume. Diatomic Gas (two atoms) Can also rotate C V = 5/2 R = 20.8 J/(K mole)

Lecture 24Purdue University, Physics 2209 Phase Transitions A phase transition occurs whenever a material is changed from one phase, such as the solid phase, to another phase, such as the liquid phase. –Phase transitions occur at constant temperature. –The latent heat of vaporization L V is the heat per unit mass that must flow to change the phase from liquid to gas or from gas to liquid. Fusion occurs when a liquid turns into a solid. Evaporation occurs when a liquid turns into a gas. Sublimation occurs when a solid changes directly to a gas without going into a liquid form.

Lecture 24Purdue University, Physics As you add heat to water, the temperature increases for a while, then it remains constant, despite the additional heat! Latent Heat L [J/kg] is heat which must be added (or removed) for material to change phase (liquid-gas). |Q| = m L Latent Heat T Q added to water water temp rises water changes to steam (boils) steam temp rises 100 o C Latent Heat Substance L f (J/kg) L v (J/kg) water33.5 x x 10 5 f=fusionv=vaporization

Lecture 24Purdue University, Physics Phase Diagram H2OH2O

Lecture 24Purdue University, Physics Phase Diagram CO 2

Lecture 24Purdue University, Physics iClicker Which can absorb more energy from your soda, a “cooler” filled with water at 0 C, or a cooler filled with ice at 0 C. A) WaterB) About SameC) Ice T Q added to water ice temp rises ice changes to water (melts) water temp rises 0 o C Latent Heat Substance L f (J/kg) L v (J/kg) water33.5 x x 10 5 Latent Heat L [J/kg] is heat which must be added (or removed) for material to change phase (liquid- gas).

Lecture 24Purdue University, Physics Exercise During a tough work out, your body sweats (and evaporates) 1 liter of water to keep cool (37 C). How much cold water would you need to drink (at 2 C) to achieve the same thermal cooling? (recall C V = 4.2 J/g for water, L v =2.2x10 3 J/g) A) 0.15 liters B) 1.0 litersC) 15 liters D) 150 liters Q evaporative = L m = 2.2x10 3 kJ/kg x 1kg Q c = c m  t = 4.2kJ/kgK x 35K x m m = 2.2x10 3 / 147 = 15kg or 15 liters!

Lecture 24Purdue University, Physics Boiling Point Going from Lafayette to Denver the temperature at which water boils: A) IncreasesB) DecreasesC) Same

Lecture 24Purdue University, Physics Exercise How much ice (at 0 C) do you need to add to 0.5 liters of a water at 25 C, to cool it down to 10 C? (L = 80 cal/g, c = 1 cal/g C)

Lecture 24Purdue University, Physics Exercise Ice cube trays are filled with 0.5 kg of water at 20 C and placed into the freezer. How much energy must be removed from the water to turn it into ice cubes at -5 C? (L = 80 cal/g, c water = 1 cal/g C, c ice = 0.5 cal/g C) Water going from 20 C to 0 C: Water turning into ice at 0 C: Ice going from 0 C to -5 C: