Physics 12 Giancoli Chapter 15 Thermodynamics

Objectives The first law of thermodynamics Deduce an expression for the work involved in a volume change of a gas at constant pressure. State the first law of thermodynamics. Identify the first law of thermodynamics as a statement of the principle of energy conservation. Describe the isochoric (isovolumetric), isobaric, isothermal and adiabatic changes of state of an ideal gas. Draw and annotate thermodynamic processes and cycles on P-V diagrams. Calculate from a P-V diagram the work done in a thermodynamic cycle. Solve problems involving state changes of a gas.

Objectives Second law of thermodynamics and entropy State that the second law of thermodynamics implies that thermal energy cannot spontaneously transfer from a region of low temperature to a region of high temperature. State that entropy is a system property that expresses the degree of disorder in the system State the second law of thermodynamics in terms of entropy changes. Discuss examples of natural processes in terms of entropy changes.

Thermodynamics The study of processes in which energy is transferred as heat and as work. Important to define the system that we are dealing with; Everything other than the system shall be referred to as the “environment” or “surroundings”.

First law of thermodynamics Otherwise known as the law of conservation of energy. Relates work/heat to the change of the internal energy of a system. What are some forms of energy that we have considered in the past? How do they relate to the conservation of energy?

First law of thermodynamics The internal energy is the sum total of all the energy of the molecules in a system. What would happen to the internal energy if heat was added to the system? If heat was taken away from the system?

First law of thermodynamics The change in internal energy ΔU of a closed system will be equal to the energy Q added to the system minus the work W done by the system on the surroundings. ΔU = Q + W

First law of thermodynamics Internal energy of an ideal gas The internal energy U is the sum of the translational kinetic energies of the atoms.

First law of thermodynamics U = N(KEavg) where N is the number of molecules of gas or N = nNA where n is the number of moles of gas and NA is Avogadro’s number The average KE of an ideal gas is given by the equation KEavg = (3/2)kBT where kB is Boltzmann’s constant and T is the temperature of the gas.

First law of thermodynamics Therefore, the internal energy of an ideal gas is given by the expression U = (3/2)NkBT where N is the number of molecules of gas kB is Boltzmann’s constant, and T is the temperature of the gas.

First law of thermodynamics ΔU = Q + W Q is the heat added to or taken away from the system. W is the work done by or on the system. What would negative signs for either Q or W imply?

First law of thermodynamics ΔU = Q + W IN OTHER WORDS… The change in energy in a system is the total of the heat and work that goes in and out of the system. Signs will make a difference.

First law of thermodynamics 2500 J of heat is added to a system, and 1800 J of work is done on the system. What is the change in internal energy of the system?

First law of thermodynamics 4300 J What would the change in internal energy be if 2500 J of heat was added to the system but 1800 J of work is done by the system?

First law of thermodynamics 700 J

First law of thermodynamics The first law of thermodynamics is one of the great laws of physics that can be proven experimentally and to which no exceptions have been seen. For simplicity’s sake, we shall discuss these laws in the context of gases.

First law of thermodynamics Consider a fixed mass of an ideal gas enclosed in a container fixed with a movable piston: (p 410 Fig 15-1). If we compress the gas (lowering the piston), what happens to its pressure and volume?

First law of thermodynamics Decreasing the volume will increase the pressure. There is a constant relationship between pressure and volume when T is constant: PV = nRT A thermodynamic process in which T is constant is called an isothermal process. p 410 Fig 15-2 constant

First law of thermodynamics What would you expect the P-V graph of an isothermal process to look like? How would the graph change if the process were to occur at a lower temperature?

First law of thermodynamics p 410 Fig 15-2 When the gas is compressed, was work done on the system or by the system?

First law of thermodynamics The act of compressing the gas is work done on the system +W. However, in order for T to remain CONSTANT the decrease in V requires an increase in pressure P which is carried out by the gas. So what is the change in internal energy of the system?

First law of thermodynamics -W = Q since ΔU = Q + W, ΔU = 0 This means that there is no change in the internal energy of the system. Does this necessarily mean that there was no work done on or by the system?

First law of thermodynamics This is an important concept in physics (wherein the net work being zero does not necessarily mean that no work was done ). In what other units have we explored this concept?

First law of thermodynamics Another thermodynamic process is one in which no heat is allowed to flow into or out of the system. This is called an adiabatic process. In terms of the eq’n for the first law of thermodynamics, which term is 0? ΔU = Q + W

First law of thermodynamics If Q = 0, what is ΔU?

First law of thermodynamics If Q = 0, and ΔU = Q + W then ΔU = W But what does this mean?

First law of thermodynamics Adiabatic expansion Quantity Value / Effect Q ΔU = Q + W = 0 + W = W V increases P ? T

First law of thermodynamics Conceptual example When you suddenly expand a rubber band, what happens when you touch it with your lips? Explain this in terms of thermodynamics.

First law of thermodynamics Conceptual example The rubber band will feel warmer than before it was stretched. When the rubber band is stretched, you do work on the system (- W). Since it was done suddenly, heat was essentially not allowed to leave the system (Q = 0). Thus, when you touch it with your lips you will feel an increase in temperature. Try it at home.

First law of thermodynamics Comparison of adiabatic and isothermal compression Quantity Isothermal Adiabatic Q ΔU V decrease P T

First law of thermodynamics Comparison of adiabatic and isothermal compression In a fuel engine, the fuel and air is compressed so rapidly (adiabatically) in the fuel piston that the T increase causes the mixture to ignite. Quantity Isothermal Adiabatic Q W ΔU -W V decrease P increase T constant

First law of thermodynamics Other thermodynamic processes that may occur are: isobaric (constant pressure) isochoric or isovolumetric (constant volume) How would you expect these processes to appear on a P-V graph?

First law of thermodynamics So far, we have discussed situations qualitatively (which is often insufficient in physics). How do we calculate the work done on a system? How have we calculated work before?

First law of thermodynamics Recall that W = Fd In terms of gases, P = F / A F = PA therefore W = PAd if Ad = ΔV then W = P ΔV

First law of thermodynamics Dimensional analysis: 1 J = 1 Nm A calculation of PΔV (using SI units) would yield (Nm-2)(m3) = Nm = J

First law of thermodynamics Comparison of thermodynamic processes

First law of thermodynamics Comparison of thermodynamic processes Constant Important characteristic Isothermal Isobaric Isovolumetric Adiabatic

First law of thermodynamics Comparison of thermodynamic processes Constant Important characteristic Isothermal T Q = -W Isobaric P ΔU = Q + W ΔU= Q + PΔV Isovolumetric V ΔV = 0 Q = ΔU Adiabatic Q = 0 ΔU = W

First law of thermodynamics Comparison of adiabatic and isothermal expansion Look at the Figure 15-3 on p 411. In which process was more work done by the gas?

First law of thermodynamics Comparison of adiabatic and isothermal expansion More work was done by the gas in the isothermal process. The average pressure is higher during the isothermal process. Work can also be represented graphically by the area under a P-V curve.

First law of thermodynamics An ideal gas is slowly compressed at a constant pressure of 2.0 atm from 10.0 L to 2.0 L (B to C). In this process, some heat flows out of the gas and the temperature drops. Heat is then added to the gas (C to A), holding the volume constant, and the pressure and temperature are allowed to rise until the temperature reaches its original value. Sketch a P-V graph of the processes involved. Calculate the total work done by the gas in the process CBA . Calculate the total heat flow into the gas.

First law of thermodynamics Graph: BC: isobaric compression (V = 10.0 L to V = 2.0 L, P = 2.0 atm ) CA: isovolumetric increase in pressure Work is done only in the compression CB. In CA, ΔV = 0 so W = 0. During CB, W = -1.6 x 103 J. Because the temperature at the beginning and end of the process is the same, ΔT = 0 so ΔU = 0. Therefore the total heat flow into the gas is -1.6 x 103 J.

First law of thermodynamics In an engine, 0.25 moles of an ideal monatomic gas in the cylinder expands rapidly and adiabatically against the piston. In the process, the temperature of the gas drops from 1150 K to 400 K. How much work does the gas do?

First law of thermodynamics 2300 J

First law of thermodynamics Recall the relationship between the heat and the change in temperature of a substance: Q = mcΔT In terms of gases, we use the expression Q = nCΔT where n is the number of moles of gas C is the molar heat capacity of the gas (this may be expressed as Cv or Cp at constant volume or pressure) and ΔT is the change in temperature of the gas

Activity Worksheet – First law of thermodynamics

Second law of thermodynamics If a hot object is placed in contact with a cold object, in which direction will heat flow?

Second law of thermodynamics Experience tells us that the heat will flow from the hot object to the cold object. Does heat flow from a colder object to a hotter object violate the first law of thermodynamics?

Second law of thermodynamics Heat flow from cold to hot does NOT violate the first law of thermodynamics but it does violate the second law of thermodynamics: Heat will flow spontaneously from a hot object to a cold object; heat will not flow spontaneously from a cold object to a hot object.

Second law of thermodynamics This concept is especially relevant in the study of heat engines.

Activity Independent study Heat engines and the Carnot cycle Handout Sections 15-5 and 15-6 of Giancoli