Heat. Heat is energy transferred between a system and its surroundings because of a temperature difference between them.

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1 What is heat? Heat

2 Heat Heat is energy transferred between a system and its surroundings because of a temperature difference between them.

3 Specific heat The specific heat of a material is the amount of heat required to raise the temperature of 1 kg of the material by 1 C. The symbol for specific heat is c. Heat lost or gained by an object is given by: Q = mc T Material c (J/(kg C)) Material c (J/(kg C)) Aluminum 900 Water (gas) 1850 Copper 385 Water (liquid) 4186 Gold 128 Water (ice) 2060

4 A change of state Changes of state occur at particular temperatures, so the heat associated with the process is given by: Freezing or melting: Q = mlf where L f is the latent heat of fusion Boiling or condensing: Q = mlv where L v is the latent heat of vaporization For water, the values are: L f = 333 kj/kg L v = 2256 kj/kg c = kj/(kg C)

5 Simulation Which graph? Heat is being added to a sample of water at a constant rate. The water is initially solid, starts at -10 C, and takes 10 seconds to reach 0 C. You may find the following data helpful when deciding which graph is correct: Specific heats for water: c liquid = 1.0 cal/g C and c ice = c steam = 0.5 cal/g C Latent heats for water: heat of fusion L f = 80 cal/g and heat of vaporization L v = 540 cal/g Which graph shows correctly the temperature as a function of time for the first 120 seconds?

6 Which graph? Which graph shows correctly the temperature as a function of time for the first 120 seconds? 1. Graph 1 2. Graph 2 3. Graph 3 4. Graph 4 5. Graph 5 6. None of the above

7 Ice water 100 grams of ice, with a temperature of -10 C, is added to a styrofoam cup of water. The water is initially at +10 C, and has an unknown mass m. If the final temperature of the mixture is 0 C, what is the unknown mass m? Assume that no heat is exchanged with the cup or with the surroundings. Use these approximate values to determine your answer: Specific heat of liquid water is about 4000 J/(kg C) Specific heat of ice is about 2000 J/(kg C) Latent heat of fusion of water is about 3 x 10 5 J/kg

8 Ice water One possible starting point is to determine what happens if nothing changes phase. How much water at +10 C does it take to bring 100 g of ice at -10 C to 0 C? (The water also ends up at 0 C.) You can do heat lost = heat gained or the equivalent method: Q = 0 micecice Tice + mwatercwater Twater =0 Plugging in numbers gives: J J (100 g) C + m 4000 ( 10 C) = 0 kg C kg C Lot's of things cancel and we're left with: 100 g = 2m, so m = 50 g. So, that's one possible answer.

9 Ice water Challenge : find the range of possible answers for m, the mass of the water.

10 Ice water Another possibility is that all the ice melts. You can do heat lost = heat gained or the equivalent method: Q = 0 micecice Tice + micelf + mwatercwater Twater =0 Plugging in numbers gives: 2000 J 4000 J (100 g) (10 C) + (100 g)( J/kg) + m ( 10 C) = 0 kg C kg C Lot's of things cancel and we're left with: 100 g 32 = 4m, so m = 800 g. So, there's another possible answer.

11 Ice water If nothing changes phase, m = 50 g. If all the ice melts, m = 800 g. Are we done? In other words, is the answer that as long as m is greater than or equal to 50 g and less than or equal to 800 g the final temperature of the mixture will be 0 C, and for all values of m outside of this range the final temperature will be something other than 0 C? 1. Yes, that is correct 2. No, at some values of m between 50 and 800 g the final temperature will be something other than 0 C. 3. No, some values below 50 g would also work. 4. No, some values above 800 g would also work.

12 Ice water If 50 g of water is enough to bring the ice to 0 C while 800 g of water is enough to bring the ice to 0 C and completely melt it, what happens for any mass of water between 50 g and 800 g?

13 Ice water If 50 g of water is enough to bring the ice to 0 C while 800 g of water is enough to bring the ice to 0 C and completely melt it, what happens for any mass of water between 50 g and 800 g? Some of the ice melts, but not all, and the final temperature of the mixture is still 0 C. Are there any other possibilities that would result in a final temperature of 0 C?

14 Ice water If 50 g of water is enough to bring the ice to 0 C while 800 g of water is enough to bring the ice to 0 C and completely melt it, what happens for any mass of water between 50 g and 800 g? Some of the ice melts, but not all, and the final temperature of the mixture is still 0 C. Are there any other possibilities that would result in a final temperature of 0 C? Yes some or all of the water could turn to ice.

15 Ice water Let s see what happens if all the water freezes. You can do heat lost = heat gained or the equivalent method: Q = 0 micecice Tice + mwatercwater Twater mwaterlf =0 Plugging in numbers gives: 2000 J 4000 J (100 g) (10 C) + m ( 10 C) m( J/kg) = 0 kg C kg C Lot's of things cancel and we're left with: 100 g 2 = 34m, so m 6 g. So, there's another possible answer.

16 Ice water, summary Amazingly, we can add anywhere from 6 g to 800 g of water at +10 C to the 100 g of ice at -10 C and get a mixture with an equilibrium temperature of 0 C. This is because the equilibrium temperature we were trying to achieve is the temperature at which liquid and solid water can co-exist, and we get such a wide ranges of possible masses because of the large amount of energy associated with a phase change.

17 Thermodynamics: a microscopic view We ll now turn to looking at thermodynamics at the level of individual molecules.

18 Avogadro s number A mole is very similar to a dozen, in the sense that it stands for a certain number of things. A dozen means 12, while a mole means 6.02 x This is also known as Avogadro's number, N A.

19 The ideal gas law An ideal gas satisfies these conditions: It consists of a large number of identical molecules. The volume occupied by the molecules themselves is negligible compared to the volume of the container they're in. The molecules obey Newton's laws of motion, and they move in random motion. The molecules experience forces only during collisions; any collisions are completely elastic, and take a negligible amount of time. Simulation

20 The ideal gas law states that: PV = nrt The ideal gas law where P is pressure, V is volume, n is the number of moles, T is the absolute temperature, and R = 8.31 J/(mol K) is the universal gas constant. The ideal gas law can be written in terms of N, the number of molecules, instead. N = n N A, so: R PV = nna T = NkT N A where k is the Boltzmann constant, 1.38 x J/K. This is the universal gas constant divided by Avogadro's number.

21 Raising the temperature The temperature of an ideal gas is raised from 10 C to 20 C while the volume is kept constant. If the pressure at 10 C is P, what is P f, the pressure at 20 C? 1. P f < P 2. P f = P 3. P < P f < 2P 4. P f = 2P 5. P f > 2P

22 Raising the temperature This is a situation in which we re using an equation (the ideal gas law) with a T, so the temperatures should be in Kelvin. The temperature of an ideal gas is raised from 283K to 293K while the volume is kept constant. If the pressure at 283K is P, what is P f, the pressure at 293K?

23 Raising the temperature This is a situation in which we re using an equation (the ideal gas law) with a T, so the temperatures should be in Kelvin. The temperature of an ideal gas is raised from 283K to 293K while the volume is kept constant. If the pressure at 283K is P, what is P f, the pressure at 293K? Not too much more than P.