Internal Energy 5.1- Thermodynamics Study of energy and its transformations Thermochemistry Study of energy changes that accompany chemical and physical changes. Energy the capacity to do work or transfer heat Internal energy total kinetic and potential energy in a system System: the part of the universe undergoing a change or being studied Surroundings: region of space around system (the rest of the universe) In any system, energy is either being stored or put in motion. System and Surroundings The system includes the molecules we want to study (here, the hydrogen and oxygen molecules). The surroundings are everything else (here, the cylinder and piston). Kinetic Energy Kinetic energy is energy an object possesses by virtue of its motion: 1 E k = mv 1
K.E. (E K )= Energy of Motion Falling Body energy released as an object travels through space. 1 E k = mv Thermal Energy energy associated with movement of compounds, atoms within compounds, atoms and subatomic particles. P.E. (E P )= Stored Energy Positional Energy Energy stored relative to a position under the influence of gravity. E P mgh Chemical Energy Energy stored in bonds. Potential Energy Potential energy is energy an object possesses by virtue of its position or chemical composition. The most important form of potential energy in molecules is electrostatic potential energy, E el : Learning Check Identify the energy in each example as 1) potential or ) kinetic. A. rollerblading B. a peanut butter and jelly sandwich C. mowing the lawn D. gasoline in the gas tank E el = KQ 1 Q d 10 Copyright 011 Pearson Education, Inc. Solution Conversion of Energy Identify the energy in each example as 1) potential or ) kinetic A. rollerblading ( kinetic) B. a peanut butter and jelly sandwich (1 potential) C. mowing the lawn ( kinetic) D. gasoline in the gas tank (1 potential) 11 Copyright 011 Pearson Education, Inc. Energy can be converted from one type to another. For example, the cyclist in Figure 5. has potential energy as she sits on top of the hill.
Conversion of Energy As she coasts down the hill, her potential energy is converted to kinetic energy. At the bottom, all the potential energy she had at the top of the hill is now kinetic energy. Conversions of chemical energy occur by: Work Energy used to move an object over some distance is work: w = F d where w is work, F is the force, and d is the distance over which the force is exerted. Conversions of chemical energy occur by: Heat Energy can also be transferred as heat. q = C s x m x T where q is heat, C s is specific heat, m is mass and T is the change in temperature. Heat flows from warmer objects to cooler objects. Internal Energy The internal energy of a system is the sum of all kinetic and potential energies of all components of the system; we call it E. Internal Energy By definition, the change in internal energy, E, is the final energy of the system minus the initial energy of the system: E = E final E initial State Functions Usually we have no way of knowing the internal energy of a system; finding that value is simply too complex a problem. 3
State Functions However, we do know that the internal energy of a system is independent of the path by which the system achieved that state. In the system depicted in Figure 5.9, the water could have reached room temperature from either direction. State Functions Therefore, internal energy is a state function. It depends only on the present state of the system, not on the path by which the system arrived at that state. And so, E depends only on E initial and E final. State Functions However, q and w are not state functions. Whether the battery is shorted out or is discharged by running the fan, its E is the same. But q and w are different in the two cases. First Law of Thermodynamics energy is neither created nor destroyed, but changes form All processes in universe are accompanied by a change in energy and since energy must remain constant: E system + E surroundings = 0 E system = -E surroundings Changes in Internal Energy If E > 0, E final > E initial Therefore, the system absorbed energy from the surroundings. This energy change is called endergonic. Changes in Internal Energy If E < 0, E final < E initial Therefore, the system released energy to the surroundings. This energy change is called exergonic. 4
There are two pathways by which energy enters or exits a system: 1. Heat transferred (q) = heat absorbed or emitted by system.. Work (w) = work done by or on surroundings by system. E state function q & w path functions E = q + w Work is defined as the energy required to move an object a distance against a force w = F d However, in chemical systems, forces are difficult to measure, so we must put work into terms we can measure Descriptive Factors of A Chemical System: (P) Pressure (V) Volume (T) Temperature (n) amount Reactivity notice no F or d Work We can measure the work done by the gas if the reaction is done in a vessel that has been fitted with a piston. w = PV Using pressure: P = F / A Rearrange for Force: F = P x A By substitution: w = P x A x d Now, to measure most chemical systems a cylinder can be used for the piston; Therefore for a cylinder: V = A x h Therefore: ΔV = A x Δh and: d = Δh So: w = P x A x Δ h 5
Therefore, by substitution: w = -P external ΔV (1L. atm = 101.3 J ) The negative sign has been added to show that work is negative (or, that energy leaves the system) So, what does this mean? By measuring P and ΔV of a chemical system, we can determine the work done on or by the system. w > 0 (+w) surrounding does work on the system (cylinder contracts) w < 0 (-w) system does work on the surrounding (cylinder expands) Remember, there are two pathways energy enters or leaves the system. One was work (w) the second is the heat transferred (q) The transfer of heat is dependent on the properties of the system described by the system s specific heat. Specific Heat Amount of heat needed to raise the temperature of 1 gram of material 1 degree centigrade. J g deg * What is the specific heat of water? * You should memorize this number (Handout) Examples of Specific Heats Calculating Specific Heat To calculate the specific heat (SH) of a substance, we measure the heat (q) in joules (J), the mass (m) in grams, and the temperature change, which is written as ΔT. (C s ) For example, the specific heat of water is 35 Copyright 011 Pearson Education, Inc. C s 6
Learning Check What is the specific heat of a metal if 4.8 g of the metal absorbs 75 J of energy and the temperature rises from 0. C to 4.5 C? Solution What is the specific heat of a metal if 4.8 g of the metal absorbs 75 J of energy and the temperature rises from 0. C to 4.5 C? STEP 1 Given 4.8 g, 75 J, ΔT = 4.3 C Need J/g C STEP Plan SH = heat g C STEP 3 Substitute the given values into equation. SH = heat (q) (mass)(t) 75 J =.6 J/g C (4.8 g)(4.3c) 37 Copyright 011 Pearson Education, Inc. 38 Copyright 011 Pearson Education, Inc. Heat Equation Rearranging the specific heat expression gives the heat equation. Heat(q) = g x C x J = J g C The amount of heat lost or gained by a substance is calculated from the mass of substance (g) temperature change (T) specific heat of the substance (J/g C) 39 Copyright 011 Pearson Education, Inc. Factors Determining Amount of Heat Transferred q = C s x m x T 1. m Amount of material Grams of material. ΔT Temperature change T = T f - T i 3. C m Molar Heat Capacity (J/moleK) Heat capacity of one mole of a substance 4. C s Specific heat (J/gK) Heat capacity of one gram of a substance Note: Remember, a chemical system is described by P, V, n, T, and reactivity based on the properties of species reacting. Notice P and V are the variables of work. Also, notice that T, n (in terms of mass) and reactivity (in terms of specific heat) are the variables of heat transferred. One common departure is the expression q = C p T where: C p is the Heat Capacity of an object C p = C s x m q < 0 (-) q = C s x m x T exothermic q > 0 (+) endothermic 7
SI unit Joule(J) the kinetic energy required to move a Kg mass a distance of one meter in one sec. From the equation of KE: J E K = ½ mv kgm s James Joule 1818-1889 calorie Commonly, energies are described in the units of calories. A calorie is the amount of heat needed to raise the temperature of 1 gram H 0, 1 degree centigrade 1 cal = 4.184 J nutritional calorie Calorie 1 Cal = 1 Kcal Learning Check How many calories are obtained from a pat of butter if it provides 150 J of energy when metabolized? Solution How many calories are obtained from a pat of butter if it provides 150 J of energy when metabolized? STEP 1 Given 150 J Need calories STEP Plan joules cal STEP 3 Equality 1 cal = 4.184 J STEP 4 Set Up Problem 150 J x 1 cal = 36 cal 4.184 J 45 Copyright 011 Pearson Education, Inc. 46 Copyright 011 Pearson Education, Inc. So: From C s, m and ΔT, we can calculate q: + q = heat gained (feels cold) - q = heat lost (feels Hot) From P and change in V, we can find w: + w = work done on system - w = work done by system Remember overall: ΔE = q + w Therefore: If Σ q + w > 0 Δ E = (+) endergonic If Σ q + w < 0 Δ E = (-) exergonic 8