Thermodynamics

Intensive and extensive properties Intensive properties: System properties whose magnitudes are independent of the total amount, instead, they are dependent on the concentration of substances Extensive properties Properties whose value depends on the amount of substance present

State and Nonstate Functions Euler’s Criterion State functions Pressure Internal energy Nonstate functions Work Heat

Energy Capacity to do work Internal energy is the sum of the total various kinetic and potential energy distributions in a system.

Heat The energy transferred between one object and another due to a difference in temperature. In a molecular viewpoint, heating is: The transfer of energy that makes use of disorderly molecular motion Thermal motion The disorderly motion of molecules

Exothermic and endothermic Exothermic process A process that releases heat into its surroundings Endothermic process A process wherein energy is acquired from its surroundings as heat.

Work Motion against an opposing force. The product of an intensity factor (pressure, force, etc) and a capacity factor (distance, electrical charge, etc) In a molecular viewpoint, work is: The transfer of energy that makes use of organized motion

Free expansion Isothermal Isochoric Isobaric Adiabatic ΔU q+w q nRT ln 𝑉𝑓 𝑉𝑖 wrev -nRT ln 𝑉𝑓 𝑉𝑖 wirrev -pextΔV

Adiabatic Changes q=0! Therefore ΔU = w In adiabatic changes, we can expect the temperature to change. Adiabatic changes can be expressed in terms of two steps: the change in volume at constant temperature, followed by a change in temperature at constant volume.

Adiabatic changes The overall change in internal energy of the gas only depends on the second step since internal energy is dependent on the temperature. ΔUad = wad = nCvΔT for irreversible conditions

Adiabatic changes How to relate P, V, and T? during adiabatic changes? Use the following equations! ViTic = VfTfc Where c = Cv/R PiViγ = PfVfγ Where γ = Cp/Cv

Adiabatic changes What about for reversible work? Wad,rev = 𝑛𝑅∆𝑇 1−γ

Free expansion Isochoric Isobaric Adiabatic Isothermal Isochoric Isobaric Adiabatic ΔU nCvΔT q+w w q nRT ln 𝑉𝑓 𝑉𝑖 or -wirrev nCpΔT or –wirrev wrev -nRT ln 𝑉𝑓 𝑉𝑖 - 𝑉𝑖 𝑉𝑓 𝑝d𝑉 𝑛𝑅∆𝑇 1−γ wirrev -pextΔV =-nCvΔT =-pextΔV ViTic = VfTfc Where c = Cv/R Cp – Cv = R PiViγ = PfVfγ Where γ = Cp/Cv

Exercise 10 g of N2 is obtained at 17°C under 2 atm. Calculate ΔU, q, and w for the following processes of this gas, assuming it behaves ideally: (5 pts each) Reversible expansion to 10 L under 2 atm Adiabatic free expansion Isothermal, reversible, compression to 2 L Isobaric, isothermal, irreversible expansion to 0.015 m3 under 2 atm Isothermal free expansion (Homework) 2 moles of a certain ideal gas is allowed to expand adiabatically and reversibly to 5 atm pressure from an initial state of 20°C and 15 atm. What will be the final temperature and volume of the gas? What is the change in internal energy during this process? Assume a Cp of 8.58 cal/mole K (10 pts) 1 cal = 4.184 J -46°C, 7.45 L

Enthalpy As can be seen in the previous derivation, at constant pressure: ΔH = nCpΔT Provided that the system does not perform additional work.

Relating ΔH and ΔU in a reaction that produces or consumes gas ΔH = ΔU + pΔV, When a reaction produces or consumes gas, the change in volume is essentially the volume of gas produced or consumed. pΔV = ΔngRT, assuming constant temperature during the reaction Therefore: ΔH = ΔU + ΔngRT

Dependence of Enthalpy on Temperature The variation of the enthalpy of a substance with temperature can sometimes be ignored under certain conditions or assumptions, such as when the temperature difference is small. However, most substances in real life have enthalpies that change with the temperature. When it is necessary to account for this variation, an approximate empirical expression can be utilized

Dependence of Enthalpy on Temperature 𝑑𝐻=𝐶𝑝𝑑𝑡 𝐻 (𝑇𝑖) 𝐻 (𝑇𝑓) 𝑑𝐻= 𝑇𝑖 𝑇𝑓 𝐶𝑝 𝑑𝑡 Where the empirical parameters a, b, and c are independent of temperature and are specific for each substance Integrate resulting equation for Cp appropriately in order to get ΔH

ΔU nCvΔT q+w w q nRT ln 𝑉𝑓 𝑉𝑖 or -wirrev nCpΔT or –wirrev wrev Free expansion Isothermal Isochoric Isobaric Adiabatic ΔU nCvΔT q+w w q nRT ln 𝑉𝑓 𝑉𝑖 or -wirrev nCpΔT or –wirrev wrev -nRT ln 𝑉𝑓 𝑉𝑖 𝑛𝑅∆𝑇 1−γ wirrev -pextΔV - 𝑉𝑖 𝑉𝑓 𝑝d𝑉 =-nCvΔT =-pextΔV ΔH 0 (for ideal gas) =ΔU + pΔV =nCvΔT =nCpΔT

Problem Calculate the change in molar enthalpy of N2 when it is heated from 25°C to 100°C. N2(g) Cp,m (J/mol K) a =28.58; b = 3.77x10-3 K; c = -0.50 x105 K2

Problem Water is heated to boiling under a pressure of 1.0 atm. When an electric current of 0.50 A from a 12V supply is passed for 300 s through a resistance in thermal contact with it, it is found that 0.798 g of water is vaporized. Calculate the per mole changes in internal energy and enthalpy at the boiling point. * 1 A V s = 1 J

Thermochemistry The study of energy transfer as heat during chemical reactions. This is where endothermic and exothermic reactions come in. Standard enthalpy changes of various kinds of reactions have already been determined and tabulated.

Standard Enthalpy Changes Defined as the change in enthalpy for a process wherein the initial and final substances are in their standard states The standard state of a substance at a specified temperature is its pure form at 1 bar Standard enthalpy changes are taken to be isothermal changes, except in some cases to be discussed later.

Enthalpies of Physical Change The standard enthalpy change that accompanies a change of physical state is called the standard enthalpy of transition Examples: standard enthalpy of vaporization (ΔvapHƟ) and the standard enthalpy of fusion (ΔfusHƟ)

Enthalpies of chemical change These are enthalpy changes that accompany chemical reactions. We utilize a thermochemical equation for such enthalpies, a combination of a chemical equation and the corresponding change in standard enthalpy. Where ΔHƟ is the change in enthalpy when the reactants in their standard states change to the products in their standard states.

Hess’s Law Standard enthalpies of individual reactions can be combined to acquire the enthalpy of another reaction. This is an application of the First Law named the Hess’s Law “The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reactions into which a reaction may be divided.”

Hess’s Law: Example

Standard Enthalpies of Formation The standard enthalpy of formation, denoted as ΔfHƟ, is the standard reaction enthalpy for the formation of 1 mole of the compound from its elements in their reference states. The reference state of an element is its most stable state at the specified temperature and 1 bar. Example: Benzene formation 6 C (s, graphite) + 3 H2(g)  C6H6 (l) ΔfHƟ = 49 kJ/mol

The temperature dependence of reaction enthalpies dH = CpdT From this equation, when a substance is heated from T1 to T2, its enthalpy changes from the enthalpy at T1 to the enthalpy at T2.

Kirchhoff’s Law It is normally a good approximation to assume that ΔrCpƟ is independent of temperature over a limited temperature range, but when the temperature dependence of heat capacities must be taken into account, we can utilize another equation

Dependence of Enthalpy on Temperature 𝑑𝐻=𝐶𝑝𝑑𝑡 𝐻 (𝑇𝑖) 𝐻 (𝑇𝑓) 𝑑𝐻= 𝑇𝑖 𝑇𝑓 𝐶𝑝 𝑑𝑡 Where the empirical parameters a, b, and c are independent of temperature and are specific for each substance Integrate resulting equation for Cp appropriately in order to get ΔH

Kirchhoff’s Law: Example

Exercise