Ideal Gas Laws and Thermodynamics PDF

Ideal Gases and the Laws of Thermodynamics Gen Physics 1 Beverly Garcia Q2- Week 7-8 Subject Teacher Most Essential Learning Competencies Enumerate the properties of an ideal gas STEM_GP12GLT-IIh-57 Solve problems in...

Ideal Gases and the Laws of Thermodynamics Gen Physics 1 Beverly Garcia Q2- Week 7-8 Subject Teacher Most Essential Learning Competencies Enumerate the properties of an ideal gas STEM_GP12GLT-IIh-57 Solve problems involving ideal gas equations in contexts such as, but not limited to, STEM_GP12GLT-IIh-58 the design of metal containers for compressed gases Interpret PV diagrams of a thermodynamic process STEM_GP12GLT-IIh-60 Compute the work done by a gas using dW=PdV STEM_GP12GLT-IIh-61 State the relationship between changes internal energy, work done, and thermal STEM_GP12GLT-IIh-62 energy supplied through the First Law of Thermodynamics Differentiate the following thermodynamic processes and show them on a PV STEM_GP12GLT-IIh-63 diagram: isochoric, isobaric, isothermal, adiabatic, and cyclic Calculate the efficiency of a heat engine STEM_GP12GLT-IIi-67 Describe reversible and irreversible processes STEM_GP12GLT-IIi-68 Explain how entropy is a measure of disorder STEM_GP12GLT-IIi-69 State the 2nd Law of Thermodynamics STEM_GP12GLT-IIi-70 Calculate entropy changes for various processes e.g., isothermal process, free STEM_GP12GLT-IIi-71 expansion, constant pressure process, etc. IDEAL GASES  GAS LAWS Boyle’s law: The relationship between the volume of a gas(fixed amount), at a constant temperature. The pressure and volume are inversely proportional to one another. In other words: Boyle's law : P1V1 = P2V2 Charles’ law shows a direct relationship between the volume of a gas and the temperature of a gas when the temperature is given in the Kelvin scale. It is the pressure that is kept constant. The volume is proportional to the temperature. This can be expressed as: Charles' law: V1 / T1 = V2 / T2 Gay- Lussac law: The pressure – temperature relationship shows a direct relationship between the pressure of a gas and its temperature, when the temperature is given in the kelvin scale. When the volume is kept constant, it is the pressure of the gas that is proportional to temperature: Gay-Lussac's law : P1 / T1 = P2 / T2 All of the above laws are combined in the ideal gas law. But what is an ideal gas? IDEAL GAS  IDEAL GAS The behavior of the gas molecules can be explained by the Kinetic Molecular Theory (KMT). It states that: a. Gases are composed of molecules. The distances from molecule to molecule are far greater than the molecules’ dimensions. These molecules can be considered as spherical bodies which possess negligible mass and volume. b. Gas molecules are always in constant random motion and they frequently collide with each other and with the walls of the container. Collisions among molecules are perfectly elastic, that is, energy may transfer from molecule to molecule as the result of collision, but the total energy of all the molecules in the system remains the same/constant. c. There is a negligible attractive or repulsive force between or among gas molecules. d. Movement of gas molecules is affected by temperature. The average kinetic of the molecules is directly related to the temperature of gas.  IDEAL GAS LAW An ideal gas is an idealized model of real gases; real gases follow ideal gas behavior if their density is low enough that the gas molecules don't interact much, and when they do interact they undergo elastic collisions, with no loss of kinetic energy. The behavior of an ideal gas, that is, the relationship of pressure (P), volume (V), and temperature (T) Ideal gas law : PV = nRT An alternate way to express the ideal gas law is in terms of N, Ideal gas law : PV = NkT where P = pressure (Pascals) V = volume (cubic meters, m3) 𝑵 n = number of moles of gas 𝒏 = R = universal gas constant (8.31 J/mol·K) 𝑵𝑶 T = temperature (Kelvin) k = Boltzmann’s constant (1.38 x10-23J/K) 1 mole = 6.022 x 1023 N = number of molecules NO = 6.022 x 1023, is known as Avogadro's number.  A mole is defined as the quantity of a substance that has the same number of particles as are found in 12-grams of carbon-12. This number, Avogadro's number, is 6.022x1023. Avogadro's number may be applied to atoms, ions, molecules, compounds, elephants, desks, or any object. It's just a convenient number to define a mole, which makes it easier for chemists to work with very large numbers of items. Example1: Counting Moles How many moles of an ideal gas are equivalent to 3.01x1024 molecules? 5 moles Example2: Moles of CO2 in a Bottle Example3: Pressurized CO2 Example4: Helium Balloon THERMODYNAMICS  Thermodynamics Thermodynamics is the study of energy transfers in a system, understood through the parameters of heat, work, and temperature. Consider this relatable example: You fill a bathtub with hot water and climb in.  Thermodynamics System In thermodynamics, the collection of objects on which attention is being focused is called the system. While everything else in the environment is called the surroundings. The system and its surroundings are separated by walls of some kind, the boundary. Thermodynamic System 3 Different Types of Thermodynamic Systems Energy and matter are Only energy is No energy or matter freely transferred transferred are transferred between it and the between the system surroundings and its surroundings Review on Energy – Internal Energy A person’s body contains internal energy. When this person undergoes rigorous exercises, part of this energy is used for the workout, and part is lost in the form of heat carried off by evaporating sweat. Processes Involving Energy Transfer 1. Heat transfer - conduction, convection, and radiation 2. Doing Work - when force causes a displacement 3. Combination of 1 and 2— involves change in the internal energy of the system Internal Energy of the System, U Internal energy, U, is the total kinetic energy and potential energy of all the molecules in the system. Kinetic energy refers to the energy associated with the motion of the particles making up the system Potential energy— refers to the energy associated with the static components of matter like chemical bonds The concepts of work, heat and the internal energy of a system are related by the first law of thermodynamics, which is an expression of the law of conservation of energy.  LAWS OF THERMODYNAMICS ❑ Zeroth Law of Thermodynamics - law that describes the behavior of a system in thermal equilibrium ❑ First Law of Thermodynamics - law that describes the behavior of the internal energy of a system; a derivation from the law of conservation of energy ❑ Second Law of Thermodynamics — law that describes irreversible and reversible processes 20  Zeroth Law of Thermodynamics 21 ZEROTH LAW of THERMODYNAMICS ZEROTH LAW of THERMODYNAMICS ILLUSTRATION 1 2 3  B A C  ZEROTH LAW of THERMODYNAMICS APPLICATION The mercury thermometer. Its contact with the human body allows both to get to thermal equilibrium. As the body sends a hit to the mercury, it dilates in the tube.  First Law of Thermodynamics Law of Conservation of Energy https://www.youtube.com/watch?v=jNPUCmkKiE4 26  FIRST LAW of THERMODYNAMICS The above expression implies The internal energy of a system changes due to heat and work. First Law of Thermodynamics is really a restatement of the law of conservation of energy. The Law of Conservation of Energy states that energy cannot be created or be destroyed; energy only changes from one form to another. The First Law of Thermodynamics states that the internal energy of a thermodynamic system tends to increase when heat is supplied to the system from the surrounding and it tends to decrease when work is performed by the system on the surrounding. 𝜟𝑼 = 𝑸 − 𝑾  FIRST LAW of THERMODYNAMICS Sign Conventions are Important !!! Heat Q is positive when the system GAINS heat and negative when the system LOSES heat. Work W is positive when it is done ON the system and negative when it is done BY the system. Example1: An insulated system takes in 6.5 kcal of heat and a 2000J work is being done to it. What is the change in the internal energy of the system? Application Example:  FIRST LAW of THERMODYNAMICS ILLUSTRATION 1 2 3 FIRST LAW of THERMODYNAMICS APPLICATION Work and heat are the transformations of energy. The energy process that converts heat energy from available sources such as chemical fuels into mechanical work is the major concern of Thermodynamics.  ACTIVITY#1: TRUE or FALSE Directions: In this activity, you will check your knowledge regarding the law of conservation of energy as presented from the lesson. 1. The law of conservation of energy states that energy can either be created or destroyed 2. A closed system is a system that has external interactions, such as energy transfers into or out of the system boundary. 3. According to the first law of thermodynamics, when heat enters or leaves a system, the system gains or loses an amount of energy equal to the amount of heat transferred. 4. A measure of energy transfer that occurs when an object is moved over a distance by an external force is known as heat. 5. The transformation of chemical energy into kinetic and heat energy by a car engine is a manifestation of the first law of thermodynamics.  ACTIVITY#1: TRUE or FALSE Directions: In this activity, you will check your knowledge regarding the law of conservation of energy as presented from the lesson. 6. An open system could not create or destroy energy. 7. Energy is a conserved quantity associated with the capacity of doing work. 8. In this modern era, it is already possible to create or build a perpetual motion machine. 9. Friction is a dissipative force that resists the relative motion of two bodies in contact and causes the loss of energy. 10. An example of the first law of thermodynamics is when a gas stove transforms chemical energy from natural gas into heat energy.  ACTIVITY#2: PROBLEM SOLVING Directions: Determine and calculate as required. Use GRESA method.  PV Diagrams and Thermodynamics Processes 36  PV DIAGRAMS ▪ Pressure-Volume Diagrams (PV Diagrams) are useful tools for visualizing thermodynamic processes of gases. ▪ Pressure on Y-axis ▪ Volume on X-axis ▪ Amount of gas remains constant. ▪ Use ideal gas law to determine temperature of gas.  PV DIAGRAMS Transition from initial to final: Volume increases, pressure decreases Work done is the area under the curve  Types of Thermodynamic PV Processes Adiabatic: Heat (Q) is not transferred into or out of the system. Isobaric: Pressure (P) remains constant. Isochoric: Volume (V) remains constant. Isothermal: Temperature (T) remains constant. ADIABATIC ISOTHERMAL (ISOTHERMIC) Adiabatic vs Isothermal ISOCHORIC or ISOVOLUMETRIC ISOBARIC  Examples Isothermal: Many machines designed to keep the temperature constant, such as refrigerators or heat pumps, follow isothermal processes Adiabatic: The cooling of air in the mountains due to the decrease in pressure as the air rises is an example of an adiabatic process Isobaric: An example of an isobaric process is the constant pressure maintained during the compression or expansion of a gas in a container Isochoric/Isovolumetric: The heating of a sealed rigid container of gas is an example of an isochoric process, as the volume remains constant Summary Types of PV/Thermodynamic Processes Summary  ACTIVITY#3: Categorizing Real-Life Systems Directions: Identify the type of thermodynamic process (if any) from the following situations described (or well approximated). 1. You let bread rise on the counter. 2. A sealed cooler of dry ice evaporates. 3. You boil water in a pressure cooker. 4. Oxygen is carried from your lungs to cells in your blood vessels. 5. A bag of chips deflates in a changing cold weather.  Second Law of Thermodynamics 50  SECOND LAW of THERMODYNAMICS The Second Law Of Thermodynamics states that heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the reverse direction. Heat flows naturally from a warmer object to a colder object, and cannot flow from a colder object to a warmer object without doing work on the system. Heat energy cannot be completely transformed into mechanical work. — Nothing is 100% efficient. All natural systems tend toward a higher level of disorder. The only way to decrease the entropy of a system is to do work on it.  SECOND LAW of THERMODYNAMICS Heat Engine Heat Engine converts internal energy into more useful forms such as mechanical energy and electrical energy  SECOND LAW of THERMODYNAMICS Heat Engine Heat engines has three essential features: 1. Heat is supplied to the engine at a relatively high input temperature from a place called the hot reservoir. 2. Part of the input heat is used to perform work by the working substance of the engine, which is the material within the engine that actually does the work (e.g. the gasoline – air mixture in an automobile engine). 3. The remainder of the input heat is rejected to a place called the cold reservoir, which has a temperature lower than the input temperature. SECOND LAW of THERMODYNAMICS Heat Engine SECOND LAW of THERMODYNAMICS Heat Engine  SECOND LAW of THERMODYNAMICS Heat Engine The work done by a heat engine is The efficiency of a heat engine is a measure of how much of the Qh is converted to work. The highest engine efficiency is 1, where no heat goes to the cold reservoir, QC = 0, that is, the whole Qh is converted to work.  SECOND LAW of THERMODYNAMICS Heat Engine What should be done to allow a heat engine to operate with maximum efficiency? Sadi Carnot, a French engineer proposed that a heat engine could have a maximum efficiency when a reversible process happens within the engine. * Reversible process: when both the system and its environment can be returned into its original states before the process occurred.  SECOND LAW of THERMODYNAMICS CARNOT Engine Carnot Engine An ideal engine developed by Sadi Carnot A heat engine that operates in a reversible cycle between the two reservoirs called the Carnot cycle. It is the most efficient of all heat engines. Carnot's Theorem: “ The efficiency of any real engine operating between two energy reservoirs will always be lower than the efficiency of a Carnot Engine operating between the same two reservoirs”  SECOND LAW of THERMODYNAMICS Efficiency of a Carnot Engine ❑ The efficiency of a Carnot Engine depends on the temperature of the two reservoirs. ❑ The temperatures must be in the Kelvin scale. ❑ All Carnot Engines operating between any two reservoirs with the same Tc and Th will have the same efficiency ❑ Efficiency is 1 (100%) if Tc = 0K. This means that there are no available cold reservoirs.  SECOND LAW of THERMODYNAMICS ENTROPY A Carnot engine has the maximum possible efficiency for its operating conditions because the process occurring within it are reversible. Irreversible processes such as friction, cause real engines to operate at less than maximum efficiency, for they reduce the ability to use heat to perform work. In general, irreversible processes cause us to lose some but not necessarily all, of the ability to perform work. This partial loss can be expressed in terms of a concept called entropy.  SECOND LAW of THERMODYNAMICS ENTROPY Entropy, like internal energy, is a function of the state of the system. Entropy is a measure of disorder. A system has low entropy if it is exhibiting high amount of order. Example: shattering of glass, melting of ice When ice melts, it becomes more disordered and Change in Entropy, ΔS less structured. The systematic arrangement of molecules in a crystal structure is replaced by a Q T = temperature in Kelvins more random and less orderly movement of S =   R = refers to the word reversible molecules without fixed locations or orientations.  T R SI unit for entropy: J/K Its entropy increases because heat transfer occurs into it. Entropy is a measure of disorder.