Thermodynamics 2 Thermodynamics The study of energy changes accompanying physical and chemical processes. From the laws of thermodynamics, one can: 1. Predict the results of chemical reactions 2. Ascertain whether or not a reaction is possible 3. Predict quantitatively the effect of changes in the experimental conditions What is Energy? 1. Kinetic Energy (KE) the energy of motion due to the motion of the system's particles (translations, rotations, vibrations) 2. Potential Energy (PE) the stored energy in an object by virtue of its position or composition (chemical bonds, electric energy of the atoms within the molecules) Energy cannot be created nor destroyed. The total energy of the universe is a constant. Energy can, however, be converted from one form to another or transferred. 3 4 Terminology: is the portion of the physical world that is selected for a thermodynamic study. Examples: A beaker of water A polluted lake is the portion of the universe with which the system interacts. Isolated = + The total energy in any isolated system is constant. All substance possess internal energy, because the molecules of all substances all have kinetic energy and potential energy. Internal energy, represented by E, is essentially the thermal energy of the particles making up the system (all the atoms or molecules of the body due to their random motion and position). It is the sum of the kinetic and potential energies of the particles that form the system. E = KE + PE 5 6 1
E = KE + PE The simplest system is an ideal gas. In an ideal gas the molecules are so far apart that intermolecular forces can be ignored. Therefore, there is no potential energy. So all the energy is kinetic. Kinetic Molecular Theory assumes that the temperature of a gas is directly proportional to the average kinetic energy of its particles. At T 1 At T 2 Calculate the internal energy of a pressurized bottle of Helium gas with volume 0.0498 m 3 at 1.01x10 7 Pa. You can use the gas law PV=nRT to express the internal energy in terms of pressure and volume: 0.368 m x 0.368 m x 0.368 m = 0.0498 m 3 T 1 < T 2 The internal energy of an ideal monatomic gas is therefore directly proportional to the temperature of the gas. E = 3 / 2 nrt R = gas constant T = temperature in Kelvin 7 (1 atm = 101.325 kpa) E = 3 / 2 nrt = 3 / 2 PV = 3 / 2 (1.01x10 7 Pa)(0.0498 m³) = 7.54 x 10 5 Pa m³ = 7.54 x 10 5 J 8 The internal energy of other systems that are more complex than the ideal gas are harder to measure. But the internal energy of the system is still has a unique value for each temperature. E = f(t) Where f is monotonically increasing function. As the temperature of the system increases, the internal energy of the system also increases. Temperature, T Use a thermometer to measure a beaker of water at room temperature. T = 21.5 C This measurement describes the state of the system at a particular moment in time. It doesn t tell us how the water got to room temperature. Temperature is a state function. 9 10 The First Law of Thermodynamics Because the internal energy of the system has a fixed value for any temperature, internal energy is also a state function. (E depends on the state of the system in terms of P, V and T.) The total energy of the universe is constant. Energy can be transferred from the system to its surroundings and vice versa, but it cannot be created nor destroyed. Any change in the internal energy of the system is equal to the difference between its initial and final values. The energy lost by the system is gained by the surroundings such that E system = E final -E initial - E system = E surroundings E universe = E system + E surroundings = 0 11 12 2
Units of Energy There are two ways to change the internal energy of a system: 1. By flow of, q Heat is the transfer of thermal energy between the system and the surroundings 2. By doing work, w Calorie: One calorie is defined as the amount of required to raise the temperature of 1 g of water by 1 degree celsius. Joule: One joule is the work done when a force of one Newton is used to move an object one meter. 1 J = 1 N m Conversion: 1 calorie = 4.184 joules Work can be converted into and vice versa. q and w are process dependent, and are not state functions. 13 14 Heat, q A form of energy Passes from one body to another as a result of a difference in temperature Heat flows from a higher temperature to a lower temperature Heat cannot be measured, but the effects which it produces is measurable. Measurement of the Effects of Heat The measurements of effects is known as calorimetry. The instrument used is the calorimeter. : the molecules inside the reaction chamber : the container holding the sample and the water bath Isolated : the calorimeter The condition under which the measurement is made is constant volume. This is a schematic of a bomb calorimeter 15 16 Experiment 8 Measure E of a combustion reaction Experiment 8 Measure E of a combustion reaction Parr Bomb Combustion of Cyclohexanol 3
Measurement of the Effects of Heat In the isolated system containing Substance A q n A T Molar Heat Capacity is the quantity of necessary to raise the temperature of one mole of the material by one degree Celsius. where n A is the number of moles of substance A T = T 2 T 1 (T 2 = final temperature, T 1 = initial temperature) Introduce a proportionality constant, C A, such that Specific Heat is the quantity of necessary to raise the temperature of one gram of the material by one degree Celsius. q = n A C A T C A is the molar capacity; it is characteristic of the substance. q = m A c A T where m A is the mass of substance A T = T 2 T 1 c A is the specific of substance A 19 20 Units of Heat Calorie: One calorie is defined as the amount of required to raise the temperature of 1 g of water by 1 degree Celsius. Heat Capacity varies as a function of temperature C A @ 100 K is not the same as C A @ 300 K Specific of water = 1.00 cal g -1 C -1 is different if the ing is done under constant pressure or under constant volume conditions Molar of water = 18.0 cal mole -1 C -1 Heat capacity measured under constant pressure is C p Heat capacity measured under constant volume is C v Conversion: 1 calorie = 4.184 joules Specific of water = 4.18 J g -1 C -1 For liquids and solids, there is little difference between C p and C v. For gas, C p > C v. 21 22 Sign Convention Example: The internal energy and temperature of a system increase (E > 0) when the system gains from its surroundings. q > 0 when is added to the substance q > 0 when T 2 > T 1 (i.e. T>0) The internal energy and temperature of a system decrease(e < 0) when the system loses to its surroundings. q < 0 when is lost by the substance q < 0 when T 2 < T 1 (i.e. T<0) 100.0 g of Pb ed to 100 C is dropped into 10.00 g of water at 0 o C. What is the final temperature? Assume that transfer is between the two substances. Specific, C p, of Pb is 0.0308 cal g -1 C -1 Specific, C p, of water is 1.00 cal g -1 C -1 Heat lost by the Pb = Heat gained by the water - q Pb = q water - m Pb c Pb (T 2 -T 1 ) Pb =m water c water (T 2 -T 1 ) water T 2 =? T 1 = 100 C T 2 =? T 1 = 0 C T 2 = 23.6 C 23 24 4
Latent Heat Effects The effects associated with changes in physical state such as fusion and vapourization are known as latent effects. Latent Heat Effects Heat of Vaporization the required to vaporize a substance at its normal boiling temperature Heat of Fusion - the required to melt a substance at its normal melting temperature - the energy required to reorganize the intermolecular structure of a substance. Heat of fusion of ice is 79.71 cal/g at 0 o C and 1 atm. Heat of vaporization of water is 539.6 cal/g 100 o C and 1 atm. Let s up 1 g of water! 25 26 Sign Convention Calculation : The internal energy and temperature of a system decrease (E < 0) when the system loses. Example 1: The internal energy and temperature increase (E > 0) when the system gains from its surroundings. HEAT A 1.00 g sample of the rocket fuel hydrazine, N 2 H 4, is burned in a bomb calorimeter containing 1200. g of water. The temperature rises From 24.62 C to 27.96 C. Taking the capacity of the calorimeter to be 200. cal C -1, calculate: (a)q for the combustion of the 1 g sample loses E < 0, q < 0 E > 0, q > 0 gains (b)the molar of combustion of hydrazine. (a) -4680 calories (b) -150. kcal/mole 27 Calculation: Example 2: When 5.00 g of sodium hydroxide is added to 100. g of water, the temperature rises from 25.0 o C to 37.5 C. Calculate the molar of reaction for the process NaOH (s) Na + (aq) + OH - (aq) taking the specific of water to be 1.00 cal g -1 C -1 and that of NaOH to be 0.48 cal g -1 C -1. Calculation: Example 3: An experiment is designed to measure the of fusion of ice. 25 g of ice at 0 C was dropped into 195 g of water at 30 C. The water is contained in a copper calorimeter of mass 100 g. The final temperature was 18 C. Given the specific of copper is 0.093 cal g -1 C -1, find the of fusion of ice. -10.2 kcal/mole Heat of fusion of ice = 80.1 cal/g 5
Calculation: Example 4: Steam at 100. C is condensed in a large calorimeter. The capacity of the calorimeter is expressed as water equivalent to 272 g. The calorimeter contains 2.82 kg of water at 5.0 C. The final temperature of 27.8 C is reached after 115 g of steam has been condensed. Find the latent of vaporization of water as given by these data. Heat of vaporization of water = 540 cal/g Work is done by the system Work is done on the system WORK Next we will talk about work! HEAT E < 0 E < 0, q < 0 E > 0 E > 0, q > 0 loses gains 32 6