1. Lecture No. 11:Heat and the First Law of Thermodynamics H. Saibi January 13, 2016

2. Outline Introduction Heat Capacity and Specific Heat Change of Phase and Latent Heat Joule’s Experiment and the First Law of Thermodynamics The internal Energy of an Ideal Gas Work and the PV Diagram for a Gas Heat capacities of Gases Heat capacities of Solids Failure of the Equipartition Theorem The Quasi-Static Adiabatic Compression of a Gas.

3. Pumping up a bicycle tire requires how much work on the air in order to compress it ???

4. Introduction 1 Energy cannot be created nor destroyed. Therefore, the total energy of the universe is a constant. Energy can, however, be converted from one form to another or transferred from a system to the surroundings or vice versa.

5. Introduction 2 Basis of the First Law of Thermodynamics: relation between heating a system, doing a work on the system, and the change in the internal energy of the system. Discussion about the role of heat that plays in the generation of motion (the cycle motion of pistons in a car, drips of water sliding down a glass of cold jus on a hot day).

6. Heat Capacity and Specific Heat Definition Heat Capacity Heat capacity: Change in internal energy required to increase the temperature of a sample by one degree. Definition Specific Heat Specific Heat (S.H.): Heat capacity per unit mass. n is the number of moles. Because C=mc, the molar specific heat c’ and specific heat c are related by: Where M =m/n is the molar mass. (6) (5a) (5b) (4) (3) (2) (1) When energy is transferred to a substance by heating it, the temperature of the substance usually increases. The amount of heat Q needed to increase the temperature of a sample of the substance is proportional to both the temperature change and the mass of the sample: Unit of heat is calorie (amount of heat needed to increase the temperature of one gram of water one Celsius degree. The calorie in term of the SI unit of energy, the joule: The British thermal unit is the Btu: The original definition of the calories implies that the S.H. of water (liquid) is: The same thing in US units is: The heat capacity per mole is called the molar specific heat c’:

7. Heat Capacity and Specific Heat Figure: Steel ingots in a twin-tube tunnel fumace. The three 53 cm diameter carbon-steel ingots seen have been heated for about 7 hours to approximately 1340 o C. Each 3200-kg ingot sits on a fumace car that transports it through the 81-m-long fumace, which is divided into 12 separate heating zones so that the temperature of the ingot is increased gradually to prevent cracking. The ingots, glowing a yellow-whitish color, exit the fumace to be melted into large, heavy-walled pipes.

8. Note:  The molar heats of all metals are about the same.  The specific heat of liquid water is larger than that of other common substances (water is an excellent material for storing thermal energy and also an excellent coolant) Heat Capacity and Specific Heat

9. Calorimetry Let m be the mass of the object, let c be its specific heat, and let T io be the initial temperature of the object. If T f is the final temperature of both the object, the water and container, the heat released by the object is: Similarly, if T iw is the initial temperature of the water and container, then the heat absorbed by the water and container is: Setting these amounts of heat equal yields an equation that can be solved for the specific heat c of the object: Because only temperature differences occur in Equation 7, and because the Kelvin and the Celsius degree are the same size, it does not matter whether we use kelvins or Celsius degrees. Where m w and c w =4.18 kJ/(kg.K) are the mass and specific heat of the water, and mc and cc are the mass and specific heat of the container. Note that temperature differences are both positive quantities, also Q in and Q out are both positive. (7)

10. Figure: Large bodies of water, such as lakes or oceans, tend to moderate fluctuations of the air temperature nearby because the bodies of water can absorb or release large quantities of heat while undergoing only very small changes in temperature. Calorimetry

11. Specific Heat

12. Change of Phase and Latent Heat The energy required to melt a sample of a substance of mass m with no change in its temperature is proportional to the mass of the sample: If the phase change is from liquid to gas, the heat required is: Where L f is called the Latent heat of fusion of the substance. At a pressure of 1 atm, the latent heat of fusion for waters is 333.56 kJ/kg=79.7 kcal/kg. (8) (9) Where Lv is called the Latent heat of vaporisation. For water at a pressure of 1 atm, the latent heat of vaporisation is 2.26 MJ/kg=540 kcal/kg. Figure: Although melting indicates that the ice has experienced a change in phase, the temperature of the ice does not change.

13. ©2008 by W.H. Freeman and Company Change of Phase and Latent Heat Note:  CO 2 does not have a liquid state at 1 atm.

14. Exercise: How much heat is needed to change 1.5 kg of ice at -20 o C and 1 atm into steam ? Figure: A 1.5 kg sample of water is heated from -20 o C to 120 o C at a constant rate of 60 kJ/min.

15. Joule’s Experiment and the First Law of Thermodynamics We can increase the temperature of a system by adding energy but we can also increase its temperature by doing work on it. Joule’s experiment establishing the mechanical equivalence of heat involved the conversion of mechanical energy into internal energy. Figure: Schematic diagram for Joule’s experiment. Insulating walls surround water. As the weights fall at constant speed, they turn a paddle wheel, which does work on the water. If friction is negligible, the work done by the paddle wheel on the water equals the loss of mechanical energy of the weights, which is determined by calculating the loss in the potential energy of the weights. Figure: Another method of doing work on a thermally insulated container of water. Electrical work is done on the system by generator, which is driven by the falling weight.

16. Joule’s Experiment and the First Law of Thermodynamics Let W on stand for the work done by the surroundings on the system. For example, suppose our system is a gas confined to a cylinder by a piston. If the piston compresses the gas, the surroundings do work on the gas and W on is positive. (however, if the gas expands against the piston, the gas does work on the surroundings and W on is negative). Also, let Q in stand for the heat transfer into the system. If heat is transferred into the system, then Q in is positive; if heat is transferred out of the system, then Q in is negative (see Figure below). Using these conventions, and denoting the internal energy by E int’ the first law of thermodynamics is written: First Law of Thermodynamics: The change in thermal energy of the system equals the heat transfer into the system plus the work done on the system. (10) Figure: Sign convention for the first law of thermodynamics

17. Joule’s Experiment and the First Law of Thermodynamics For very small amounts of heat absorbed, work done, or changes in internal energy, it is customary to write Equation 10 as: In this equation, dE int is the differential of the internal-energy function. However, neither dQ in nor dW on is a differential of any function. Instead, dQ in merely represents a small amount of energy transferred to or from the system by heating or cooling, and dW on represents a small amount energy transferred to or from the system by work being done on or by the system. (11)