Heat

1. Heat

2. Kinetic Theory of Matter • Proposes that heat is a measure of the internal kinetic energy (microscopic jiggles) of the molecules and atoms making up the substance. • The precise relationship between the average molecular kinetic energy KEave and absolute temperature T is found to be KEave = (3/2) kT Where K, known as Boltzmann constant has the value k = 1.38 x 10-23 J/K

3. Heat • A measure of the total kinetic energy of a system. • Internal energy in transit from one body of matter by virtue of a temperature difference between them. • Unit of Measurement: Joule, kcal, Btu • Kilocalorie • The amount of heat required to raise the temperature of 1 kg of water by 1°C.

4. Relationship between joule and kilocalorie 1 J = 2.39 x 10-4 kcal 1 kcal = 4185 J

5. Quantity of Heat Heat lost or gained = mass x c x Temperature change Q = m c ∆T Where: Q is the heat lost or gained in kcal m is the mass in kg, c is the specific heat kcal/kg⁰C ∆T is the temperature change in ⁰C • If you are given c in cal/g ⁰C; this works when heat is in calories, mass in grams, temperature in ⁰C.

6. Example • How much heat must be added to 5 kg of water to increase its temperature by 20 ⁰C? The specific heat of water is 1cal/g ⁰C. • Given: m = 5kg or 5000g c = 1 cal/g ⁰C ∆T = 20 ⁰C Solution: Q = m c ∆T = 5000g x 1 kcal/g ⁰C x 20⁰C = 100000kcal

7. Specific Heat • The movement of molecules depends on the type of material used. • Property of a material that explains why some foods and liquids remain hotter longer than others.

8. Specific Heat and Water • Water has one of highest specific heats at 1cal/g ⁰C. • One gram of water is able to absorb and hold more heat than other liquids. • When water is cold, it can absorb more heat as it warms up.

9. 11.2.5 Thermal Equilibrium • Occurs when one or more substances reach a common temperature by exchanging heat. Heat lost = Heat gained Qlost =Qgained For example, if you put ice in warm water, the warm water gets cold, the ice gets warm, and melts. When the ice completely melts, they will all have the same temperature. They are in equilibrium.

10. A 0.5-kg aluminum block at 75⁰C is dropped into a cup of water with a mass of 2.0 kg at 40⁰C and comes to thermal equilibrium. What is the final temperature (Tf) of the water and aluminum? The specific heat of aluminum is 0.21 kcal/kg⁰C. Given: Aluminum Block Water mAl = 0.5kg mwater = 2.0kg cAl = 0.21 kcal/kg⁰Ccwater = 1kcal/kg⁰C TiAl = 75⁰C Tiwater = 40⁰C

11. The initial temperature of the aluminum block is greater than the initial temperature of water. Since heat flow is form hot to cold, then the aluminum block will lose heat, while water will gain heat. • Aluminum block will lose heat; ∆TAl = (Ti–Tf) = 75⁰C – Tf • Water will gain heat; ∆Twater = (Tf - Ti) = Tf - 40⁰C

12. Apply the equilibrium condition: Qlost =Qgained mAl x cAlx ∆TAl = mwater x cwater x ∆Twater (0.5kg)(0.21 kcal/kg⁰C)(75⁰C – Tf) = (2kg)(1 kcal/kg⁰C)(Tf - 40⁰C)

13. 11.2.6 Transmission of Heat • Conduction • Convection • Radiation

14. 11.2.6.1 Conduction • Conduction involves the transfer of heat through direct contact • Heat conductors conduct heat well, insulators do not Example of Conduction

15. 11.2.6.2 Convection • Takes place in liquids and gases as molecules move in currents • Heat rises and cold settles to the bottom Example of Convection

16. 11.2.6.3 Radiation • Heat is transferred through space • Energy from the sun being transferred to the Earth Example of Radiation

17. 11.2.7 Change in State • When the atoms and molecules are no longer closely associated with one another, all bonds have been broken and the liquid has become a gas.

18. 11.2.7.1 Melting and Heat of Fusion In melting, it takes an amount of heat Qf = m Hf to change from a solid to a liquid Where: Qf = amount of heat to melt the solid in kcal Hf = heat of fusion in kcal/kg m = mass of the solid in kg

19. 11.2.7.2 Evaporization and Heat of Vaporization In evaporating, it takes an amount of heat Qv = m Hv to change from a liquid to a gas Where : Qv= amount of heat to evaporate the liquid in kcal Hv= heat of vaporization in kcal/kg m = mass of the liquid in kg

20. 11.2.7.3 Sublimation • More rarely, the solid can change directly to a gas.

21. 11.2.7.4 Equation for Change of State The amount of heat needed to turn mass of ice at some initial temperature into a gas at a final temperature can be computed by the following : Isuyatkora 

22. 11.3 Thermodynamics • What we’ve learned thus far about heat and thermal energy is summed up in the laws of thermodynamics. The word thermodynamics stems from Greek for “movement of heat.” • Is a branch of physics looking at how changes in energy. Work and the flow of heat influence each other.

23. 11.3.1.1 The First Law • Whenever heat flows into or out of a system, the gain or loss of thermal energy equals the amount of heat transferred. Mathematically speaking, Total Heat = change in internal energy + work done

24. 11.3.1.2 The Second Law It is impossible for heat to flow from a point of lower temperature to a point of higher temperature without the application of energy from an external source.

25. 11.3.1.3 Entropy • Is a measure of the amount of wasted heat in the system. • It is measure of the amount of disorder in the system. Entropy change = heat added / Temperature (in K )