# Thermodynamics II The First Law of Thermodynamics

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Thermodynamics II The First Law of Thermodynamics
Heat and Work. First Law of Thermodynamics Heat and Work on Quasi-Static Processes for a Gas. The Second Law of Thermodynamics Heat Engines and the Second Law of Thermodynamics Refrigerators and the Second Law of Thermodynamics The Carnot Engine Heat Pumps Irreversibility and disorder. Entropy References: Tipler; wikipedia,…

Surroundings System The First Law of Thermodynamics
Energy exists in many forms, such as mechanical energy, heat, light, chemical energy, and electrical energy. Energy is the ability to bring about change or to do work Thermodynamics is the study of energy. Surroundings The system can interchange mass and energy through the frontier with the environment. An example of “closed system” - no mass flow- is the gas confined in a cylinder. The frontier –in this case physical- is made by the cylinder and the piston walls. System The frontier of the system is arbitrarily chosen

First Law of Thermodynamics → Conservation of Energy:
The First Law of Thermodynamics First Law of Thermodynamics → Conservation of Energy: Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another. The First Law of Thermodynamics (Conservation) states that energy is always conserved, it cannot be created or destroyed. In essence, energy can be converted from one form into another. The energy balance of a system –as a consequence of FLT- is a powerful tool to analyze the interchanges of energy between the system and its environment. We need to define the concept of internal energy of the system, Eint as an energy stored in the system. Warning: It is no correct to say that a system has a large amount of heat or a great amount of work

The First Law of Thermodynamics. Heat, Work and Internal Energy
Joule’s Experiment and the First Law of Thermodynamics. Equivalence between work and heat 1 calorie = Joules Work is done on water. The energy is transferred to the water – i. e. the system- . The energy transferred appears as an increment of temperature. We can replace the insulating walls by conducting walls. We can transfer heat through the walls to the system to produce the same increment of temperature. The increment of temperature of the system reflects the increase of Internal Energy. Internal energy is a function of state of the system Schematic diagram for Joule´s experiment. Insulating walls to prevent heat transfer enclose water. As the weights fall at constant speed, they turn a paddle wheel, which does work on water. If friction in mechanism is negligible, the work done by the paddle wheel on the water equal the change of potential energy of the weights. The sum of the heat transfer into the system and the work done on the system equals the change in the internal energy of the system

The First Law of Thermodynamics
Another method of doing work. Electrical work is done on the system by the generator, which is driven by the falling weight.

The state of the gas will be described by the Ideal Gas-Law.
The First Law of Thermodynamics. Application to a particular case: A gas confined in a cylinder with a movable piston The state of the gas will be described by the Ideal Gas-Law. How the confined gas interchange energy (heat and work) with the surroundings?. How can we calculate the energy –heat and/or work- transferred, added of subtracted, to the system? What is the value of the internal energy for the gas in the cylinder First Law “Quasi static processes”: a type of processes where the gas moves through a series of equilibrium states. Then, we can apply the IGL. In practice, if we move slowly the piston, will be possible to approximate quasi-static processes fairly well.

Rn – H – λET – G – D - Ph = ΔEint
First Law of Thermodynamics. Fluxes of energy and mass on the earth surface. Energy balance. H λET CO2 Rn = Rns + Rnl D G ΔE Ph Energy fluxes: Rn : Net gain of heat energy from radiation λET Latent heat, Energy associated to the flux of water vapor leaving from the system H Sensible Heat G Heat energy by conduction to the soil Ph: Net photosynthesis ΔEint: Change of the internal energy of the system D: Advection Net fluxes of mass Water vapor Carbon –CO2 Energy balance (applying First Law): Rn – H – λET – G – D - Ph = ΔEint

The First Law of Thermodynamics
The First Law of Thermodynamics. Application to a particular case: A gas confined in a cylinder with a movable piston. Internal Energy Internal Energy for an Ideal Gas Only depends on the temperature of the gas, and not of its volume or pressure What is the value of the internal energy for the gas in the cylinder? Experiment: Free expansion For a gas at low density – an ideal gas-, a free expansion does not change the temperature of the gas. If heat is added at constant volume, no work is done, so the heat added equals the increase of thermal energy Internal Energy is a state function, i.e. it is not dependent on the process, only it depends of the initial and final temperature

Heat transferred to a system
The First Law of Thermodynamics. Application to a particular case: A gas confined in a cylinder with a movable piston. Heat Heat transferred to a system If heat is added at constant pressure the heat energy transferred will be used to expand the substance and to increase the internal energy. If the substance expands, it does work on its surroundings. Applying the First Law of Thermodynamics If heat is added at constant volume, no work is done, so the heat added equals the increase of thermal energy The expansion is usually negligible for solids and liquids, so for them CP ~ CV.

Heat transferred to a system. A summary
The First Law of Thermodynamics. Application to a particular case: A gas confined in a cylinder with a movable piston Heat transferred to a system. A summary Heat energy can be added (or lost) to the system. The value of the heat energy transferred depends of the process. Typical processes are - At constant volume - At constant pressure For the case of ideal gas Relationship of Mayer From the Kinetic theory, for monoatomic gases for biatomic gases Ideal Gas For solids and liquids, as the expansion at constant pressure is usually negligible CP ~ CV. Adiabatic: A process in which no heat flows into or out of a system is called an adiabatic process. Such a process can occur when the system is extremely well insulated or when the process happens very quickly.

The First Law of Thermodynamics
The First Law of Thermodynamics. Application to a particular case: A gas confined in a cylinder with a movable piston. Work Work done on the system, Won , is the energy transferred as work to the system. When this energy is added to the system its value will be positive. The work done on the gas in an expansion is P- V diagrams Constant pressure If 5 L of an ideal gas at a pressure of 2 atm is cooled so that it contracts at constant pressure until its volume is 3 l, what is the work done on the gas? [405.2 J]

P- V diagrams Isothermal
The First Law of Thermodynamics. P-V diagrams P- V diagrams Isothermal Conecting an initial state and a final state by three paths Constant pressure Constant Volume Constant Temperature

The First Law of Thermodynamics
A biatomic ideal gas undergoes a cycle starting at point A (2 atm, 1L). Process from A to B is an expansion at constant pressure until the volume is 2.5 L, after which is cooled at constant volume until its pressure is 1 atm. It is then compressed at constant pressure until the volume is again 1L, after which it is heated at constant volume until it is back in its original state. Find (a) the work, heat and change of internal energy in each process (b) the total work done on the gas and the total heat added to it during the cycle. A system consisting of 0.32 mol of a monoatomic ideal gas occupies a volume of 2.2 L, at a pressure of 2.4 atm. The system is carried through a cycle consisting: The gas is heated at constant pressure until its volume is 4.4L. The gas is cooled at constant volume until the pressure decreased to 1.2 atm The gas undergoes an isothermal compression back to initial point. (a) What is the temperature at points A, B and C (b) Find W, Q and ΔEint for each process and for the entire cycle

Adiabatic Processes. No heat flows into or out of the system
The First Law of Thermodynamics. Processes. P-V Diagrams Adiabatic Processes. No heat flows into or out of the system

Adiabatic Processes. No heat flows into or out of the system
The First Law of Thermodynamics. Processes. P-V Diagrams Adiabatic Processes. No heat flows into or out of the system The equation of curve describing the adiabatic process is We can use the ideal gas to rewrite the work done on the gas in an adiabatic process in the form A quantity of air is compressed adiabatically and quasi-statically from an initial pressure of 1 atm and a volume of 4 L at temperature of 20ºC to half its original volume. Find (a) the final pressure, (b) the final temperature and (c) the work done on the gas cP = J/(mol•K); cV = J/(mol•K). M=28.84 g

The First Law of Thermodynamics. Processes. P-V Diagrams
A polytropic process is a thermodynamic process that obeys the relation: PVn = C, where P is pressure, V is volume, n is any real number (the polytropic index), and C is a constant. This equation can be used to accurately characterize processes of certain systems, notably the compression or expansion of a gas, but in some cases, possibly liquids and solids. For certain indices n, the process will be synonymous with other processes: if n = 0, then PV0=P=const and it is an isobaric process (constant pressure) if n = 1, then for an ideal gas PV= const and it is an isothermal process (constant temperature) if n = γ = cp/cV, then for an ideal gas it is an adiabatic process (no heat transferred) if n = ∞ , then it is an isochoric process (constant volume)

The First Law of Thermodynamics. Cyclic Processes. P-V Diagrams
Two moles of an ideal monoatomic gas have an initial pressure P1 = 2 atm and an initial volume V1 = 2 L. The gas is taken through the following quasi-static cycle: A.- It is expanded isothermally until it has a volume V2 = 4 L. B.- It is then heated at constant volume until it has a pressure P3= 2 atm C.- It is then cooled at constant pressure until it is back to its initial state. (a) Show this cycle on a PV diagram. (b) Calculate the head added and the work done by the gas during each part of the cycle. (c) Find the temperatures T1, T2, T3 Solve the above problem considering the STEP A is an adiabatic expansion. Determine the efficiency of the both cycles. Determine the efficiency of a Carnot cycle operating between the temperature extremes of the both cycles..

The First Law of Thermodynamics. Cyclic Processes. P-V Diagrams

The First Law of Thermodynamics. Cyclic Processes. P-V Diagrams
At point D in figure the pressure and temperature of 2 mol of an ideal monoatomic gas are 2 atm and 360 K. The volume of the gas at point B on the PV diagram is three times that at point D and its pressure is twice that a point C. Paths AB and DC represent isothermal processes. The gas is carried through a complete cycle along the path DABCD. Determine the total work done by the gas and the heat supplied to the gas along each portion of the cycle

The First Law of Thermodynamics. Cyclic Processes. P-V Diagrams

The First Law of Thermodynamics. Cyclic Processes. P-V Diagrams

Second Law of Thermodynamics. Heat Engines
Heat Engines and the Second Law of Thermodynamics Refrigerators and the Second Law of Thermodynamics The Carnot Engine Heat Pumps Irreversibility and disorder. Entropy A steamboat or steamship, sometimes called a steamer, is a ship in which the primary method of propulsion is steam power

Second Law of Thermodynamics. Heat Engines
Zeroth Law → Temperature First Law of Thermodynamics → Energy balance on the system (Conservation of Energy) What are the rules to obtain useful energy (those that drives a machine,…)? Why the heat flows spontaneously from the hotter body to the colder one? Second Law of Thermodynamics No system can take energy as heat from a single source and convert it completely into work without additional net changes in the system or in the surroundings SECOND LAW, KELVIN STATEMENT A process whose only net result is to transfer energy as heat from a cooler object to a hotter one is impossible SECOND LAW, CLAUSIUS STATEMENT

Schematic drawing of a steam engine.
Second Law of Thermodynamics. Heat Engines. Steam Engine A heat engine is a cyclic device whose purpose is to convert as much heat input into work as possible. Working substance (water in steam engine, air and gasoline vapor in internal-combustion engine), that absorbs a quantity of heat, Qh, does work on its surroundings, and gives an amount of heat, Qc, as it returns to initial state. Schematic drawing of a steam engine. Several hundreds atmospheres and water vaporizes at about 500 ªC

Second Law of Thermodynamics. Heat Engines. Internal-Combustion Engine
Otto cycle representing the internal-combustion engine

Second Law of Thermodynamics. Heat Engines.
No system can take energy as heat from a single source and convert it completely into work without additional net changes in the system or in the surroundings SECOND LAW, KELVIN STATEMENT Efficiency of a heat engine It is impossible to make a heat engine with a efficiency of 100 per cent It is impossible for a heat engine working in a cycle to produce only the effect of extracting heat from a single reservoir and performing an equivalent amount of work

Schematic representation of a refrigerator.
Second Law of Thermodynamics. Refrigerators. Heat Pumps Schematic representation of a refrigerator. COP. Coefficient of Performance of a Refrigerator

COP. Coefficient of Performance of a Refrigerator
Second Law of Thermodynamics. Refrigerators. A process whose only net result is to transfer energy as heat from a cooler object to a hotter one is impossible SECOND LAW, CLAUSIUS STATEMENT It is impossible for a refrigerator working in a cycle to produce only the effect of extracting heat from a cold object and reject the same amount of heat to a hot object COP. Coefficient of Performance of a Refrigerator

The objective of a heat pump is to heat a region of interest
Second Law of Thermodynamics. Refrigerators. Heat Pumps The objective of a heat pump is to heat a region of interest Useful energy Heat Pump COPHP. Coefficient of Performance of a Heat pump

Second Law of Thermodynamics
Second Law of Thermodynamics. Equivalence of the Heat Engine and Refrigerator Statements

Maximum efficiency for a heat engine. The Carnot Engine
What is the maximum possible efficiency for a heat engine working between two heat reservoirs? Carnot Theorem No engine working between two given heat reservoirs can be more efficient than a reversible engine working between those two reservoirs Carnot engine: A reversible engine working in a cycle between two heat reservoirs. The cycle is called a Carnot cycle

Maximum efficiency for a heat engine. The Carnot Cycle
Carnot cycle is a reversible cycle between only two heat reservoirs 1.- A quasi-static isothermal absorption of heat from a heat reservoir 2.- A quasi-static adiabatic expansion to a lower temperature 3.- A quasi-static isothermal exhaustion of heat to a cold reservoir 4.- A quasi-static adiabatic compression back to the original state

Maximum efficiency for a heat engine. The Carnot Cycle
Carnot cycle is a reversible cycle between two heat reservoirs Isothermal processes Adiabatic processes

Second Law of Thermodynamics
Second Law of Thermodynamics. Maximum efficiency for a Heat Engine; Maximum COP for a Refrigerator and for a Heat Pump A steam engine works between a hot reservoir at 100 ºC and a cold reservoir at 0ºC. (a) What is the maximum possible efficiency of this engine? If the engine is run backwards as refrigerator, what is its maximum coefficient of performance? If the engine is running as heat pump, what is the maximum coefficient of performance?

Second Law of Thermodynamics. Irreversibility, desorder: Entropy
The free expansion of an ideal-gas: No work, no heat, no change of internal energy,… But, is it the same state after and before of the free expansion? Entropy, S: a physical magnitude whose net increment (system + surroundings) indicates the irreversibility of a process: In a irreversible process, the entropy of the universe increases For any process, the entropy of the universe never decrease A spontaneous heat transfer (from hotter body to a colder one) implies an increment of entropy (It is a irreversible process) Entropy: a thermodynamic function of disorder

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