Introduction to the First Law Chapter 2

1. Introduction to the First LawChapter 2 CHEM 321-01

2. Thermodynamics What is thermodynamics? • “The study of the transformation of energy” • Thermo – heat, dynamics – patterns of change • Deals with conversion of energy • Deals with direction of energy change • Developed mostly in the 19th century (1800’s) after the general acceptance of Dalton’s atomic theory (1808) but before the development of quantum mechanics which implies that the microscopic universe of atoms and electrons follow different rules than the macroscopic rules of large masses. • Deals mostly with the “bulk” properties of large collections (ensembles) of atoms and molecules. • Macroscopic rules for the transfer of energy.

3. Applications of Thermodynamics Applications: • Initially developed from observations of scientists and engineers trying to develop more efficient steam engines. • Heating and cooling • Refrigeration • Development of new types of batteries • Engine efficiency • Energy transfer in biological systems • Protein folding and molecular stability

4. Basic Concepts • System • The region of space that we are interested in studying. • Surroundings • The region outside of the system from which we make our observations. • Universe • System + surroundings

5. Types of Systems • Depends on the characteristic of the boundary which separates the system from the surroundings. • Open System • Allows matter and energy to pass between the system and surroundings. • Closed System • Allows energy, but not matter, to pass between the system and surroundings. • Isolated System • Neither matter nor energy can pass between the system and surroundings.

6. Work • Work (w) • The movement of an object a distance (s) against an opposing force by means of an applied force (F). • Mathematically, it is the dot product of the distance vector with the applied force vector: where θis the angle between the vectors. • Is a scalar quantity, having no direction. • The transfer of energy involving organized motion. When work is performed by a system on the surroundings, the molecules in the surroundings experience an orderly motion. When work is done on a system, molecules in the surroundings are used to transfer energy in an organized way to the system.

7. Heat • Heat (q) • Energy transferred between the system and its surroundings as a result of a temperature gradient. • Involves random motion (thermal motion) of molecules.

8. Heat Boundaries Types of Boundaries • Diathermic • Allows for the transfer of heat between the system and surroundings if there is a temperature gradient. • Adiabatic • Does not allow the transfer of heat between the system and surroundings.

9. Heat Transfer Processes • Exothermic Process • Process that releases energy as heat. • In a diathermic system, increases temperature of surroundings. • In an adiabatic system, increases temperature of system. • Endothermic Process • Process that absorbs energy as heat. • In a diathermic system, decreases temperature of the surroundings. • In an adiabatic system, decreases temperature of system.

10. Internal Energy • Internal Energy (U) • The total energy of a system, including both the kinetic and potential energy of the molecules in the system. • Does not include the kinetic energy arising from the motion of the system as a whole, such as its kinetic energy as it accompanies the Earth on its orbit around the Sun. • Is an extensive property – a property that depends on the amount of matter (number of moles). The more molecules, the greater the internal energy.

11. Units of Energy • Internal Energy, Work, and Heat are related • Energy is the capacity to do work. • Work is the way to transfer that energy between the system and surroundings through the organized motion of matter. • Heat is the way to transfer that energy between the system and surroundings through the disorderly motion of matter. • All have the same units – the Joule (J). • Other units of internal energy, work, and heat: • Electronvolt (eV) • The amount of kinetic energy acquired by an electron that is accelerated across a potential difference of 1 V. • Calorie (cal) • The amount of energy required to raise the temperature of 1 gram of water by 1 C.

12. Changes in Internal Energy • Change in Internal Energy (DU) • The change in internal energy as a system goes from an initial state with an internal energy Uito a final state with an internal energy Uf. • The internal energy of a system may be increased by: • Doing work (w ) on the system. • Transferring energy as heat (q ) to the system. • Heat and work are equivalent ways of changing the internal energy of a system. • If a system is isolated from its surroundings, then no change in internal energy takes place:

13. First Law of Thermodynamics • First Law of Thermodynamics • “For an isolated system, the total energy (internal energy) remains constant.” • Law of Conservation of Energy. • The total energy of a system can ONLY be changed by an organized transfer (work) or disorderly transfer (heat) of energy between the system and surroundings. • Mathematically, q – energy transferred as heat to the system. w – work done on the system. Sign of q and w are from the standpoint of the system. If positive, system acquires energy. If negative, system releases energy.

14. ΔU for Isolated Systems • In an Isolated System • No matter can be transferred between the system and surroundings. • No energy can be transferred (by work or heat) between the system and surroundings. • Thus, q = 0 and w = 0, and

15. ΔU for Closed Systems • In an Closed System • No matter can be transferred between the system and surroundings. • Energy can be transferred (by work or heat) between the system and surroundings. • If q > 0 and w > 0, heat and work are transferred to the system. • If q < 0 and w < 0, energy is lost from the system as heat and work.

16. ΔU for Adiabatic Systems • In an Adiabatic System • Heat can not be transferred between the system and surroundings. • q = 0 • Thus,

17. First Law of Thermodynamics • First Law of Thermodynamics • “The work needed to change an adiabatic system (q = 0) from one specified state (Ui)to another specified state (Uf)is the same however the work is done.” • The change in internal energy (ΔU) can be determined by measuring the work (wad) needed to bring about a change in an adiabatic system.

18. State and Path Functions • State function • Properties that are independent of how a state is prepared. • Functions of variables that define the current state of a system, such as pressure, temperature, and volume. • Internal energy (U) is a state function. • Path function • Properties that relate to the path or preparation of a state. • The work (w) done in preparing the state and the energy transferred as heat (q) are path functions. • Since systems do not possess work or heat, but perform or transfer them, they are not properties of the current state of the system, but refer to the path taken by the system in attaining the current state. • The work is different if the change takes place adiabatically or nonadiabatically.

19. Exact Differentials • An infinitesimal change in the internal energy of a system is represented as the differential, dU. • For a complete process, dU is integrated from the initial to the final conditions. • Mathematically, • When dU is integrated, the result is the change in internal energy for the process. • dU is an exact differential because its integrated value of ΔU is path-independent. • All state function have exact differentials.

20. Inexact Differentials • Infinitesimal changes in the work or heat of a system are represented as the differentials, dw and dq. • For a complete process, dw and dq are integrated from the initial to the final conditions. • Mathematically, • Whendw and dq are integrated, the result is the absolute amount of work and heat for the process. • The differentials dw and dq are called inexact differentials because their integrated values w and q are path-dependent.

21. Infinitesimal Changes • For an infinitesimal change in the system: • Integration from initial to final conditions gives: • Which is the mathematical expression for the First Law of Thermodynamics.

22. Expansion Work • Expansion work • Work arising from a change in volume, including compression. • In classical mechanics, the total work (w) necessary to move an object a displacement of (dz) against an opposing force (F) is: • Negative sign denotes that the system doing the work will have a decrease in internal energy.

23. Expansion Work • Considering the mechanical work performed by an expanding gas confined in a frictionless, massless, rigid, perfectly-fitting piston: • A is the area of the cross section of the piston. • pext is the external pressure against which the piston moves. • dV is the infinitesimal change in volume of the piston during the course of expansion.

24. Expansion Work • If the external pressure (pext) is constant, we can integrate from an initial volume (Vi) to a final volume (Vf): where

25. Free Expansion • If there is no external pressure (pext), or opposing force, the system experiences a free expansion. • Occurs when a gas expands into a vacuum, a region of space with no pressure. • Because pext = 0 for a free expansion, the work (w) performed by the system is:

26. Reversible Expansion • Reversible Process – • A process during which the system is never more than infinitesimally far from equilibrium (mechanical and thermal). • During a reversible process, the system remains at equilibrium with the surroundings at all times. • An infinitesimal change in the external conditions of the surroundings causes an infinitesimal change in the system. • The infinitesimal change in the system can be reversed by an infinitesimal return to the external conditions of the surroundings. • In reality, reversible processes can not be achieved because it would take an infinite amount of time to carry out a series of infinitesimal changes. A reversible process is an idealization. • Irreversible Process – • A process which cannot be reversed by an infinitesimal change in the external conditions. • During an irreversible process, the system makes a finite departure from equilibrium. • All real processes are irreversible processes.

27. Reversible Expansion • Reversible Expansion – • A expansion in infinitesimally small steps so that the system remains at mechanical equilibrium with the surroundings during the course of the expansion. • In this case, the internal pressure of the piston (p) equals the external pressure (pext) of the surroundings during the course of the expansion: • The work of reversible expansion (wrev) is: • Because the external pressure is not constant throughout the course of the expansion, it cannot be brought outside of the integral.

28. Isothermal Reversible Expansion • Isothermal Reversible Expansion – • A reversible expansion performed at constant temperature in which the system is in contact with a constant thermal surroundings. • For a reversible expansion of a perfect gas in a piston: • The work of reversible expansion (wrev) is: • The pressure is related to the volume by:

29. Isothermal Reversible Expansion • The reversible expansion work (wrev) is: • Because the gas is confined and the temperature is constant, n and T are constants, and the work is: • Evaluating the integral gives:

30. Isothermal Reversible Expansion • The reversible expansion work (wrev) of a perfect gas is: • During an expansion (when vf > vi), wrev < 0, meaning that the system has performed work on the surroundings and the internal energy of the system has decreased. • Because the process is at constant temperature, there is a compensating influx of energy as heat, so overall the internal energy is constant. • Also, more work is done for a given change in volume at higher temperatures.

31. Isothermal Reversible Expansion • Consider an indicator diagram that compares a reversible isothermal expansion to an irreversible expansion against a constant external pressure. • More work is obtained for a reversible expansion than for an irreversible expansion. • Matching the external pressure to the internal pressure at each state of the process ensures that none of the “pushing power” is wasted. • If pext > p, compression occurs, and there is a decrease in the amount of work done. • If p > pext, the “pushing power” is wasted. • Represents the maximum available work for a system between specific initial and final states and for a specific path. • Using Boyle’s Law, the work for isothermal reversible expansion in terms of pressures:

32. Heat Transactions • The First Law of Thermodynamics may also be expressed as – • dq – infinitesimal change in heat energy transferred across a diathermic boundary. • dwexp– infinitesimal amount of energy as work due to gas expansion. • dwe – additional work (such as electrical work of driving a current through a circuit). • If no additional work is applied, dwe= 0. • If the gas is confined to a vessel of constant volume (rigid walls), the gas cannot expand and cannot perform any expansion work, dwexp = 0. • In this case: • Subscript V denotes a constant-volume condition. • For a measurable finite change: • If qv > 0, heat is applied to the system. • If qv < 0, system loses heat to surroundings.

33. Calorimetry • Calorimetry – the study of heat transfer during physical and chemical processes. • Calorimeter – a device for measuring the heat transferred. • Specific heat capacity (s) • The amount of heat required to raise the temperature of one gram of a substance by one degree Kelvin (or Celsius). • Intensive property of the material composing the system. • Materials with a low specific heat, such as many metals, need little heat for a relatively large change in temperature. • Heat capacity (C) • The amount of heat required to raise the temperature of a given quantity of the substance by one degree Kelvin (or Celsius). • Extensive property, depends on the amount of material. • The relationship between the heat capacity and the specific heat capacity of a substance is: wherem is the mass of the substance in grams.

34. Heat and Heat Capacity • The amount of heat (q) that has been absorbed or released by a particular substance undergoing a change in temperature (ΔT) is: where (C) is the heat capacity of the substance.

35. Adiabatic Bomb Calorimetry • The absolute internal energy (U) of a system cannot be measured directly. • “No work or heat meters.” • However, the change in internal energy (ΔU) due to the transfer of heat may be measured by an adiabatic bomb calorimeter. • Adiabatic – no heat transfer between the system and surroundings. • Bomb – a sturdy vessel (usually very thick stainless steel) that maintains a constant volume and withstands very high pressure. • Used to study combustion reactions and explosions.

36. Adiabatic Bomb Calorimetry • How does it work? • A known mass of a sample is placed inside the “bomb” and the bomb is pressurized with O2 with a high pressure (~30 atm). • The bomb is immersed in a stirred water bath. The combined device is the calorimeter (system). • The calorimeter is also immersed in an outer water bath (surroundings). The temperature of both the outer and inner water bath are monitored and adjusted to the same temperature during the course of the combustion reaction. As a result, there is no heat transfer between the calorimeter and outer water baths, and the process is adiabatic.

37. Adiabatic Bomb Calorimetry • How does it work? • The heat (qV)released or absorbed is proportional to the change in temperature (ΔT). Thus, a measurable ΔT causes a measurable ΔU: • The proportionality constant (CV), calorimeter constant, is the constant-volume heat capacity of the calorimeter. • Unique to each calorimeter (bomb + inner bath). • Must be determined by calibrating the calorimeter by either: • Measured electrically by passing a current (I) from a source of known potential (V) through a heater for a period of time (t). • By burning a known mass of standard substance (benzoic acid), that has a known heat output.

38. Heat Capacity and Internal Energy • Increasing the temperature increases the internal energy (U) of the system. • The slope of the tangent to the curve is defined as the heat capacity at constant volume. • Formally defined, the heat capacity at constant volume is: • This is a partial derivative, which is a slope with all variables except one held constant.

39. Heat Capacity and Internal Energy • The internal energy (U) of the system actually varies with volume and temperature. • The heat capacity at constant volume (CV) varies with both volume and temperature. • Temperature-dependence of heat capacity: • Heat capacity decreases with lower temperature. • Over small temperature changes above 298 K, variations in the heat capacity are small, and it can be considered to be temperature-independent. In this case: • If the heat capacity is independent of temperature over the range of temperatures of interest, a measurable ΔT causes a measurable ΔU a measurable in a constant-volume system:

40. Heat Capacity and Internal Energy • For a fixed quantity of heat: • A large heat capacity implies that there will be only a small increase in temperature, and the sample has a large capacity for heat. • An infinite heat capacity implies that there will be no increase the system’s temperature no matter how much heat is supplied to the system. • At a phase transition (melting or boiling point), the temperature does not rise as heat is supplied. Thus, at the temperature of a phase transition, the heat capacity of a sample is infinite. • Molar heat capacity at constant volume, (CV, m) • heat capacity per mole of material. • an intensive property.

41. Enthalpy • For a system that is not at constant volume, ΔU is not equal to the heat supplied, as for a fixed-volume system. • Under these circumstances, some of the energy supplied as heat to the system causes the gas to expand, performing expansion work on the surroundings. As a result, dU <dq . • The enthalpy ,H, is defined as: where U, p, and V are the internal energy, pressure, and volume of the system, respectively. Since these parameters are all state functions, the enthalpy is also a state function. • An infinitesimal change in enthalpy (dH) is related to infinitesimal changes in the internal energy (dU), pressure (dp) , and volume (dV) of the system by:

42. Enthalpy • Applying the Product Rule for the differentiation of two functions: • From the First Law, • The infinitesimal change in enthalpy (dH) becomes: • If the system is at constant pressure, or isobaric condition, then dp = 0, the infinitesimal change in enthalpy (dH) :

43. Enthalpy • The infinitesimal change in enthalpy (dH) for a system at constant pressure is: • Moreover, if the system is at mechanical equilibrium with the surroundings at constant pressure p , then only expansion work is being done: • The infinitesimal change in enthalpy (dH) becomes:

44. Enthalpy • The enthalpy change (ΔH ) for a measurable amount of heat at constant pressure: • An enthalpy change can be measured calorimetrically by monitoring the temperature change that accompanies a physical or chemical change occurring at constant pressure. • Isobaric calorimeter – a calorimeter that maintains a constant pressure. • Two types of isobaric calorimeters: • Adiabatic flame calorimeter • Differential scanning calorimeter

45. Enthalpy Change for a Perfect Gas • The enthalpy of a perfect gas is related to its internal energy by: • This implies that the measurable change in enthalpy in a reaction that produces or consumes gas at constant temperature is: • where Δng is the change in the number of moles of gas during the reaction.

46. Enthalpy Change for a Perfect Gas • Consider the combustion of hydrogen gas to form water: • Three moles of gas are replaced with two moles of liquid. • So Δng = 0 – 3 = -3 moles. At 298 K, • Why is the difference negative? • Heat escapes from the system during the reaction (ΔH < 0), but the system contracts as the liquid is formed. Energy is returned to the system from the surroundings in the form of work, increasing the internal energy (ΔU > 0).

47. Temperature Dependence of Enthalpy • The enthalpy (H) of a substance increases as the temperature increases. • The relation between the increase in enthalpy and the increase in temperature depends on the condition of constant pressure: • Consider the plot of enthalpy versus temperature at constant pressure: • The slope of the tangent to the curve is defined as the heat capacity at constant pressure (Cp), and is an extensive property. • Formally defined, the heat capacity at constant pressure is: • The molar heat capacity at constant pressure (Cp,m) is an intensive property and is the heat capacity per mole of material.

48. Temperature Dependence of Enthalpy • The heat capacity at constant pressure (Cp) is used to relate the change in enthalpy to a change in temperature. • For an infinitesimal change in temperature, dT, the corresponding infinitesimal change in enthalpy (dH) at constant pressure is: • For a measurable change in temperature, ΔT, the measurable change in enthalpy (ΔH ) at constant pressure is: • The molar heat capacity at constant pressure(Cp,m) varies with temperature. • The variation can be ignored under a small temperature range. • Under larger temperature ranges, a convenient approximate empirical expression is: • where the coefficients a, b, and c are independent of temperature and unique for each substance.

49. Relationship between Cp and CV • For a given increase in temperature, the enthalpy (H) of a system will increase more than the internal energy (U). • At constant pressure, most systems expand when heated, and do work on the surroundings, decreasing the internal energy (U). Thus, some of the energy supplied as heat is returned to the surroundings as work. • As a result, the temperature of the system rises less than when the heating occurs at constant volume. • This implies that the constant-pressure heat capacity is larger than the constant-volume heat capacity: • For a perfect gas, the relationship between the two heat capacities is:

50. Adiabatic Changes • An adiabatic change occurs when the system is isolated from the surroundings and heat (q) is not allowed to pass between them. • For an adiabatic process, dq = 0. • From the First Law of Thermodynamics: • Since dq = 0, the infinitesimal change in internal energy (dU) is: where the subscript denotes an adiabatic process. • For an adiabatic process, work is completely converted into internal energy.