PPT 107 PHYSICAL CHEMISTRY

1. PPT 107 PHYSICAL CHEMISTRY Semester 2 Academic session 2012/2013

2. CHAPTER 2FIRST LAW OF THERMODYNAMICS

3. THERMODYNAMIC SYSTEM Characterized by the 4 laws of thermodynamics

5. CHAPTER 2First law of thermodynamics

6. Key Concepts • Work • Pressure-Volume Work (P-V Work) • Heat • First Law of Thermodynamics • Enthalpy • Perfect Gas • Molecular Nature of Internal Energy

7. Units • The General Conference on Weights and Measures recommended a single system of units for use in science. This system is called the International System of Units , abbreviated SI. • The SI uses meters (m) for length, kilograms (kg) for mass, and seconds (s) for time. A force that produces an acceleration of one meter per square second when applied to a one-kg mass is defined as one newton(N): • SI units for some quantities: pressures would always be given in [newtons / square meter]: (pascals), cubic meters for volume, kg/cubic m for density, kelvins for temperature, moles for amount of substance, and kg/mol for molar mass. • However, it seems clear that many scientists will continue to use such units as atmospheres and torrs for many years to come. The current scientific literature increasingly uses SI units, but since many non-SI units continue to be used, it is helpful to be familiar with both SI units and non-SI units.

8. WORK Work (w) is defined as the force (F) that produces the movement of an object through a distance (d): Work is done when and object, e.g. a system's wall, moves against an opposing force. This is equivalent to an ordered motion done by the system on the surroundings or vice versa. Work = force ×distance w = F x d Work also has units of J, kJ, cal, kcal, Cal, etc.

9. Suppose a force F acts on a body while the body undergoes an infinitesimal displacement dx in the x direction. The infinitesimal amount of work dw done on the body by the force F is defined as: the units of work are those of force times length. The SI unit of work is the joule (J). Power P is defined as the rate at which work is done. If an agent does work dw in time dt, then P =dw/dt. The SI unit of power is the watt (W): 1 W=1 J/s

11. P-V work Work in thermodynamics is defined as in classical mechanics. When part of the surroundings exerts a macroscopically measurable force F on matter in the system while this matter moves a distance dx at the point of application of F, then the surroundings has done work [dw=Fx dx] on the system, where Fx is the component of F in the direction of the displacement. F may be a mechanical, electrical, or magnetic force and may act on and displace the entire system or only a part of the system. When Fx and the displacement dx are in the same direction, positive work is done on the system: dw>0. When Fx and dx are in opposite directions, dw is negative.

13. Pressure-volume (P-V) work The work done in a volume change is called P-V work By removing weights and decreasing the pressure and allowing the volume to adjust according to Boyle's law with no heat addition By holding the pressure constant and increasing the volume by heating the gas using Charle’s law Changing the volume by 2 ways OR Initial state Final state Final state

14. [dw=Fx dx] F = PA dw = PA dx dwrev= -P dVclosed system, reversible process where 1 and 2 are the initial and final states of the system, respectively

15. Pressure-volume work • The example of PV work – in the cylinder of an automobile engine • The combustion of the gasoline causes gases within the cylinder to expand, pushing the piston outward and ultimately moving the wheel of the car. The relationship between a volume change (ΔV) and work (w): • W= -P ΔV • Where P is external pressure • The units of PV work are L·atm; 1 L·atm = 101.3 J. • If the gas expands, ΔV is positive, and the work term will have a negative sign (work energy is leaving the system). • If the gas contracts, ΔV is negative, and the work term will have a positive sign (work energy is entering the system). • If there is no change in volume, ΔV = 0, and there is no work done. (This occurs in reactions in which there is no change in the number of moles of gas.)

16. Work done by gas The units of PV work are L·atm; 1 L·atm = 101.3 J. if ΔV < 0, then W > 0.; increases in volume means work done BY the system on the environment. if ΔV > 0, then W < 0.; decreases in volume means work done by the environment ON the system.

17. Work and heat are not state functions On a graph of pressure versus volume, the work is the area under the curve that describes how the state is changed from State 1 to State 2. A curved black line from State 1 to State 2 represents a change brought about by removing weights and decreasing the pressure and allowing the volume to adjust according to either Boyle’s law (the line is curved and the amount of work done on the gas is shown by the red shaded area below this curve) or Charle’s law (the resulting change in state proceeds from State 1 to an intermediate State "a" on the graph by heating. State "a" is at the same pressure as State 1, but at a different volume. If we then remove the weights, holding a constant volume, we proceed on to State 2. The work done in this process is shown by the yellow shaded area).

18. Using either process we change the state of the gas from State 1 to State 2. But the work for the constant pressure process is greater than the work for the curved line process. The work done by a gas not only depends on the initial and final states of the gas but also on the process used to change the state. Different processes can produce the same state, but produce different amounts of work. Notice that not only does the work done by the gas depend on the process, but also the heat transferred to the gas. In the first process, the curved line from State 1 to State2, no heat was transferred to the gas; the process was adiabatic. But in the second process, the straight line from State 1 to State "a" and then to State 2, heat was transferred to the gas during the constant pressure process.  The heat transferred to a gas not only depends on the initial and final states of the gas but also on the process used to change the state.

19. What are Reversible and Irreversible Processes? • There are two main types of thermodynamic processes: the reversible and irreversible. The reversible process is the ideal process which never occurs, while the irreversible process is the natural process that is commonly found in the nature. Therefore: • The reversible process is an idealization. • All real processes on Earth are irreversible. P-V Work REVERSIBLE IRREVERSIBLE A reversible process is one that can be halted at any stage and reversed. In a reversible process, the system is at equilibrium at every stage of the process. An irreversible process is one where it cannot be halted at any stage and reversed and the system is not always at equilibrium at every stage of the process.

20. What is a Reversible Process? The process in which the system and surroundings can be restored to the initial state from the final state without producing any changes in the thermodynamics properties of the universe is called a reversible process. In the figure below, let us suppose that the system has undergone a change from state A to state B. If the system can be restored from state B to state A, and there is no change in the universe, then the process is said to be a reversible process. The reversible process can be reversed completely and there is no trace left to show that the system had undergone thermodynamic change.

21. For the system to undergo reversible change, it should occur infinitely slowly due to infinitesimal gradient. During reversible process, all the changes in state that occur in the system are in thermodynamic equilibrium with each other. Thus there are two important conditions for the reversible process to occur. Firstly, the process should occur in infinitesimally small time and secondly all of the initial and final state of the system should be in equilibrium with each other. If during the reversible process the heat content of the system remains constant, i.e. it is adiabatic process, then the process is also isentropic process, i.e. the entropy of the system remains constant. The phenomenon of undergoing reversible change is also called reversibility. In actual practice the reversible process never occurs, thus it is an ideal or hypothetical process.

22. What is an Irreversible Process? The irreversible process is also called the natural process because all the processes occurring in nature are irreversible processes. The natural process occurs due to the finite gradient between the two states of the system. For instance, heat flow between two bodies occurs due to the temperature gradient between the two bodies; this is in fact the natural flow of heat. Similarly, water flows from high level to low level, current moves from high potential to low potential, etc. Here are some important points about the irreversible process: In the irreversible process the initial state of the system and surroundings cannot be restored from the final state. During the irreversible process the various states of the system on the path of change from initial state to final state are not in equilibrium with each other. During the irreversible process the entropy of the system increases decisively and it cannot be reduced back to its initial value. The phenomenon of a system undergoing irreversible process is called as irreversibility.

23. Calculation of PV work for reversible processes The integral (2.28) is called a line integral. The value of the line integral (2.28) is defined as the sum of the infinitesimal quantities P(T, V)dVfor the particular process used to go from state 1 to state 2. This sum equals the area under the curve that plots P versus V. Figure 2.3 shows three of the many possible ways in which we might carry out a reversible volume change starting at the same initial state (state 1 with pressure P1and volume V1) and ending at the same final state (state 2).

24. In process (a), we first hold the volume constant at V1 and reduce the pressure from P1 to P2 by cooling the gas. We then hold the pressure constant at P2 and heat the gas to expand it from V1 to V2.

25. In process (b), we first hold P constant at P1 and heat the gas until its volume reaches V2. Then we hold V constant at V2 and cool the gas until its pressure drops to P2.

26. In process (c), the independent variables V and T vary in an irregular way, as does the dependent variable P.

28. Example for P-V WORK Inflating balloon requires the inflator to do pressure-work on the surroundings. If balloons is inflated from a volume of 0.100L to 1.85L against an external pressure of 1.00 atm, how much work is done (in joules)? Answer: ΔV = V1 -V2 = 1.85L -0.100L = 1.75L W= -P ΔV = -1.00 atm x 1.75L = -1.75L.atm Convert to Joule: -1.75L.atm x 101.3 J= -177 J 1L.atm The work is negative because it is being done by the system as its volume increases due to the expansion of the gas into the much bigger volume.

29. Study Example 2.2 page 44 Find the work for processes (a) and (b) of Fig. 2.3 if P1 3.00 atm, V1 500 cm3, P2 1.00 atm, and V2 2000 cm3. Figure 2.3 The work w done on the system in a reversible process (the heavy lines) equals minus the shaded area under the P-versus-V curve. The work depends on the process used to go from state 1 to state 2. Use this equation: Simple as the previous example. Processes (a) and (b) are expansions. Hence the system does positive work on its surroundings, and the work w done on the system is negative in these processes. Answer: = - 152 J and = -456 J

33. HEAT • Heat is a exchange of thermal energy between a system and its surroundings caused by temperature difference. • Notice the distinction between heat and temperature. Temperature is a measure of the thermal energy of a sample matter. Heat is transfer of the thermal energy. • Heat may be defined as energy in transit from a high temperature object to a lower temperature object. • Anytime two substances with different temperatures come in contact with each other, there is an energy transfer. One substance loses heat energy and the other substance gains heat energy. • Heat energy flows from a hotter substance to a colder substance.

34. Let bodies 1 and 2 have masses m1 and m2 and initial temperatures T1 and T2, with T2 > T1 ; let Tf be the final equilibrium temperature. Provided the two bodies are isolated from the rest of the universe and no phase change or chemical reaction occurs, one experimentally observes the following equation to be satisfied for all values of T1 and T2: where c1 and c2 are constants (evaluated experimentally) that depend on the composition of bodies 1 and 2. We call c1 the specific heat capacity (or specific heat) of body 1. We define q, the amount of heat that flowed from body 2 to body 1, as equal to m2 c2 (T2-Tf).

35. The unit of heat commonly used in the nineteenth and early twentieth centuries was the calorie (cal), defined as the quantity of heat needed to raise one gram of water from 14.5°C to 15.5°C at 1 atm pressure. (This definition is no longer used, as we shall see in Sec. 2.4.) By definition, 1.00 cal/(g °C) at 15°C and 1 atm. Once the specific heat capacity of water has been defined, the specific heat capacity c2 of any other substance can be found from the above relation by using water as substance 1. When specific heats are known, the heat q transferred in a process can then be calculated from above relation.

36. The specific heat capacities of substances are functions of temperature and pressure. When an infinitesimal amount of heat dqp flows at constant pressure P into a body of mass m and specific heat capacity at constant pressure cp, the body’s temperature is raised by dT and where cp is a function of T and P. Summing up the infinitesimal flows of heat, we get the total heat that flowed as a definite integral: The pressure dependence of cp was omitted because P is held fixed for the process. The quantity mcp is the heat capacity at constant pressureCp of the body: Cp ≡ mcp.

37. Equation to be more accurately written as: If the dependence of cp2 and cp1 on T is negligiblethe above eq can be reduces to original eq. The heat can be transferred reversibly or irreversibly. A reversible transfer of heat requires that the temperature difference between the two bodies be infinitesimal. When there is a finite temperature difference between the bodies, the heat flow is irreversible.

38. For example, if the ice cube in the diagram is placed in the container of water, there is an energy transfer. The hotter substance loses heat energy and the colder substance gains heat energy. The water and its container lose heat energy and become cooler. The ice cube gains heat energy and becomes warmer (this causes the ice cube to melt). According to the law of energy conservation the total heat energy lost by the water and its container is equal to the total heat energy gained by the ice. Heat can be transferred reversibly or irreversibly. A reversible transfer of heat requires that the temperature difference between the two bodies be infinitesimal. When there is a finite temperature difference between the bodies, the heat flow is irreversible.

40. Heat capacity when system absorbs heat (q) its temperature changes by ΔT: Experimental measurements demonstrate that the heat absorbed by a system and its corresponding temperature change are directly proportional: qαΔT. The constant of proportionality between q and ΔT is called the heat capacity. Heat capacity (C) is the amount of heat (q) a substance must absorb to raise its temperature(ΔT) by 1 °C.-Heat capacity has units of J/°C (or J/K), and is an extensive property, depending on the sample size.

41. Specific Heat Capacity The specific heat (c, or specific heat capacity, Cs) of an object, is the quantity of heat required to change the temperature of 1 gram of a substance by 1°C (or K): Specific heat has units of J/g°C, and is an intensive property, which is independent of the sample size.

42. Example Calculate the amount of heat needed to increase the temperature of 250g of water from 20oC to 56oC. Answer: q = m x Cg x (Tf - Ti) m = 250g Cg = 4.18 J oC-1 g-1 (from table)Tf = 56oC Ti = 20oC q = 250 x 4.18 x (56 - 20) q = 250 x 4.18 x 36 q = 37 620 J = 38 kJ

43. What is the difference between heat capacity and specific heat? Heat capacity is the amount of heat required to raise the temperature of any quantity of substance by 1 degree centigrade.Specific heat is the amount of heat required to raise the temperature of 1kg (MASS) of substance by 1 degree substance. The unit for specific heat is J/(g*K). The unit for heat capacity is J/K. Difference between specific heat capacity and heat capacity is identical to difference between concentration and amount of substance - one is intensive, other extensive property.

44. Is the law of conservation of Energy.

45. 1st Law = Conservation of Energy The first law of thermodynamics is simply an expression of the conservation of energy principle. The principle of the conservation of energy states that energy can neither be created nor destroyed.  But it can change from one type of energy to another (for example kinetic to potential) but the total amount remains fixed (The total energy of a closed system remains constant.)

46. In thermodynamics, energy is classified into three different types: • work (W) • heat (Q) • internal energy (ΔU) • This allows us to write a simple form for conservation of energy (or the first law of thermodynamics) as (the change in the internal energy of a closed system is equal to the amount of heat supplied to the system, minus the amount of work performed by the system on its surroundings) The standard unit for all these quantities would be the joule.

47. ENERGY • Energyis defined as the ability or capacity to do work on some form of matter (the amount of work one system is doing on another). There are several forms of energy: • Potential energy is the energy that a body possesses as a consequence of its position in a gravitational field (e.g., water behind a dam). • Kinetic energy is the energy that a body possesses as a consequence of its motion (e.g., wind blowing across a wind generator). It is dependent upon an object's mass and velocity (e.g., moving water versus moving air). • Internal energy is the total energy (potential and kinetic) stored in molecules. It is the energy associated with the random, disordered motion of molecules; it refers to the invisible microscopic energy on the atomic and molecular scale. The First Law of Thermodynamics states that energy lost during one process must equal the energy gained during another, i.e., all energy is conserved.

48. Unit of Energy • Energy is measured in Joules (J) or Calories (cal).1 J = 1 kg m2s-2 • A calorie (cal) is the amount of energy needed to raise the temperature of 1 g of water by 1°C. 1 cal = 4.184 J

49. INTERNAL ENERGY The internal energy, U of a system is the sum of the kinetic and potential energies of all the particles that compose the system or the total energy of a system (the energy associated with the random, disordered motion of molecules). It involves energy on the microscopic scale.  The total (internal) energy in a system includes potential and kinetic energy.  • Binding energies – atomic bonds • (potential energy from intermolecular forces) • translational kinetic energy • vibrational and rotational kinetic energy

50. There are two ways to change the internal energy: with workand  heat. • Internal energy of an object can be changed by the following methods: • It increases if energy is added to the system. • i.e. by heating or by doing work on the system. • It decreases if energy is removed from the system or work is done by the system. • i.e. Thus heat and work changes the internal energy of an object.