ES190: Thermodynamics Notes PDF

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Meng School of Engineering Laura Fernández-Cuervo Medrano University of Warwick uES190 ThermodynamicsMODULE OUTLINE:Lecture 1: Introduction to thermodynamicsThermodynamics: ​ theory of the reactions between heat and mechanical/electrical/chemical... energy, and of the conversion of either into the o...

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Meng School of Engineering University of Warwick

Laura Fernández-Cuervo Medrano u1814983

ES190 Thermodynamics MODULE OUTLINE:

Lecture 1: Introduction to thermodynamics Thermodynamics: theory of the reactions between heat and mechanical/electrical/chemical... energy, and of the conversion of either into the other. Thermodynamics deals with large scale properties (e.g. volume of a gas, pressure, etc) without considering the microscopic structure, so it looks at the macroscopic structure Laws of Thermodynamics: - Four commonly accepted “laws” of thermodynamics - We will meet the zeroth, first and second in this course. Example: steam turbine power plant

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Important equations relating component inputs and outputs

Thermodynamic systems: - System: portion of universe we select for investigation - Surroundings: everything outside the system - Boundary: what separates system from surroundings

- Open system: allows mass in/out - Closed system: does not allow mass to enter or leave the system ENERGY CAN ENTER/LEAVE IN BOTH SYSTEMS Adiabatic walls: w  alls that prevent thermal interaction in a system. There is no energy transfer across these walls Diathermal walls: walls that allow thermal interaction in a system. Systems separated by a diathermal wall are in “thermal contact” Complicated example: an air conditioning unit (closed system). Important to define the system of interest, could be a whole unit or individual components

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Types of thermodynamic variables: - Intensive: v ariables which are essentially local in character. Intensive variables are those that do not depend on system size (e.g. pressure, electric field, temperature) - Extensive: variables which correspond to the same measure of the system as a whole. These depend on the size of the system as they are proportional to the mass of the system (if intensive variables are held constant) Be ‘specific’: lower case variables often indicate ‘specific’ quantities, i.e. per unit mass example: - U: internal energy [J] - u: specific internal energy, i.e. internal energy per unit mass [J/kg] Systems: - Simple systems: The whole system is homogeneous (e.g. gas/piston in a cylinder). The state of a simple system is completely known if we know the values of just two independent variables e.g. pressure and volume

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Complex systems: Systems which are not simple. This may be because there is more than one phase present in the system (e.g. a glass of water with ice cubes).

Types of equilibrium: All three balls are said to be in mechanical equilibrium - Metastable equilibrium: stable for small displacements but not for larger ones If there is a change in a system, it reconfigures until no further changes take place. When no further changes occur, system has reached equilibrium - If no interactions from outside the system boundary and its state is unchanging, system is in equilibrium - We cannot define the state of a simple system if it is not in equilibrium. Process: change in the state of a system If the process can be reversed so that the system and surroundings return to initial state, process is reversible.

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Lecture 2: Mechanical and electrical work Mechanical work: Work = force x distance moved in the direction of force

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[Nm = J] Work done BY a system - p  ositive Work done ON the system - n  egative

Work in mechanical systems: We often assume zero friction and zero inertia Therefore, WORK IN = WORK OUT

so work is conserved

Mechanical work: transient quantity which is associated with the transfer of energy into or out of a system. Work is not a property of a system. A body does not ‘have’ a certain amount of work in it. Mechanical power: rate at which work is done [J/s = Watts, W]

Energy: (General definition: capacity of a physical system to do work) Quantity that if it crosses the system boundary, changes the state of a closed system - Work done = energy transferred - W = average force x distance moved Consider an expanding fluid contained by a piston and a cylinder (closed system)

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Before expansion: F = pA ; (the gas exerts a force on the piston head) as p=F/A After expansion: F - dF = (p - dp)A ; (area unchanged, force reduces by a little bit, and so does the pressure) So work done dW = average force x distance moved 4

So:

dW = pAdx, where Adx = dV, which is a small change in the volume of system dW = pdV

If process continues via series of small expansions of dx, where V1 is the initial volume and V2 is the final volume This assumes the process is quasistatic* Assumptions: - Force F was only allowed to differ from the force pA infinitesimally - This means that gas was in e  quilibrium at all times - The process from state 1 (V 1 ) to state 2 (V 2 ) is r eversible Quasistatic processes: One in which the system passes through a continuous series of equilibrium states. - A reversible process does not suffer any hysteresis, (there can be no frictional or viscous forces). - Direction of this process can be reversed by a reverse infinitesimal change in the conditions of the system Reversible process on p-V diagram: Graph shows how p and V change for the gas. The line joining 1 and 2 is a series of equilibrium states- p  rocess

Irreversibility: Irreversible process: work done is less than that done in a reversible process

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Electrical work: Electrons moving across a system boundary do work on the system Electrical work: work done by an electron. Given by its charge (e) multiplied by the potential difference it moves through (V) W = eV There are 1/e electrons per Coulomb of charge, so W = QV [J] Electrical power: Q = It, therefore, as W electrical = IVt, Power = IV Kilowatt hour (kWh): is a unit of energy which means 1kW of power each hour (not a SI unit). 1kWh = 1000W x 60mins x 60s = 3600000 J = 3.6 MJ Efficiency:

In an ideal electrical/mechanical system, efficiency = 1, so Win = Wout For an ideal system involving electrical+mechanical work:

IDEAL SITUATIONS: Ideal electric motor:

The negative sign before the electrical power term indicates that electrical work is done on the system. Ideal generator:

The negative sign before the mechanical power term indicates that mechanical work is done on the system. 6

Ideal transformer:

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Energy: from electrical to magnetic to electric Assume no losses and reversibility Voltage ratio depends on turns ratio:

Dealing with alternating currents: The mean value of both V and I over a full period equals 0, but we can use the root mean square (rms) value:

Lecture 3: Heat, temperature and energy storage Heat: As well as work, heat is another method of energy transfer. - If systems A and B are put into thermal communication and their states/properties change, then there has been heat transfer. - Heat is energy, just like work. Denoted by Q, measured in [J]. Joining wall is diathermal, not adiabatic

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Rotating paddle does work on system, changing its state. Original state restored by placing the system in thermal contact with a second system.

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Heat: like work, it is a transient phenomenon that crosses a system boundary, causing a change in the equilibrium state of the system. It does not act via movement of the system boundary. Energy is transferred via molecular collision or electromagnetic radiation. - Heat INTO a system - p  ositive Q - Heat OUT OF a system - n  egative Q Heat transfer: - Conduction: due to molecular collision. - Radiation: energy transfer by electromagnetic waves. Although convection is commonly regarded as means of heat transfer, strictly speaking, it is a combination of conduction and mass transfer. - Heat is a form of energy that crosses system boundaries (by conduction or radiation) and changes the state of a system. ZEROTH LAW OF THERMODYNAMICS If 2 objects (A and B) are both in thermal equilibrium with a third object (C), then A and B are in thermal equilibrium. - Thus, if A and B are brought into contact, there is no heat flow between them. - Zeroth law establishes the existence of temperature. Temperature: Is related to (not equal to) the average kinetic energy of a molecule in the system. Temperature scale: - At “absolute zero” a substance essentially has no internal energy. - “Absolute scales” start at absolute zero (e.g. Kelvin scale) Conversions: K = ºC + 273 ºC = K - 273 ºF = 32 + 1.8ºC

T absolute zero = 0 K / -273 ºC / -460 ºF T melting ice = 273 K / 0 ºC / 0 ºF T boiling water = 373 K / 100 ºC / 212 ºF

States of matter: matter exists in different phases (solid, liquid, gas). Solid: - Well ordered - Vibrational energy only - Stays where it is put Liquid: - More disordered - Vibrational, rotational and translational energy - Needs containment in most directions, but intermolecular attractive forces on average still exceed inertia forces Gas: - Even more disordered - Vibrational, rotational and translational energy - Needs containment in all directions These are sometimes referred to as phases , but these are more specific as in some materials there can be multiple phases of one state. PROBLEM SET 1 COVERED UP TO HERE 8

Heat capacity: Ratio of the amount of heat energy transferred to an object to the resulting increase in its temperature. Specific heat capacity (c) : of a substance, is the amount of energy E required to raise the temperature of a unit mass of a substance by unit temperature rise, as E=mcΔӨ For many liquids, change in internal energy (ΔU) is prop to change in temp (ΔT) The constant of proportionality is called the specific* heat capacity (c) of a substance;  c = specific heat capacity [J kg -1   K-1  ]. -1 C = thermal capacity [J K ] - heat required to increase system temp. by 1 K. (C = mc). -

cp: specific heat capacity at constant pressure. cv: specific heat capacity at constant volume.

c water = 4.2 kJ/kg/K*

Storage of energy: When we talk about storing thermal energy what we really mean is that we are changing the internal energy of the store, increasing it when heat goes in and decreasing it when energy is removed. W  ays of storing energy: - Springs (not explained in this section) - Flywheels - Potential energy storage - Batteries - Capacitors Storage options for large amounts of energy are rather limited, so energy storage is a hugely important research area at present Flywheels: transfer excess E k  to a rotating mechanical device

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Need flywheel to have substantial moment of inertia (I).

Storage as potential energy: GPE = mgh In practice this usually involves using excess electricity to pump water up a hill and generating hydroelectricity when it comes back down again. Batteries: These store limited amounts of chemical energy, which may be converted to electrical energy. These are described as primary (non-rechargeable) or secondary (chargeable). The power efficiency from charge to discharge is typically 75% for lead acid batteries. Capacitors: Can be used to store electrical charge. - The energy stored = ½CV2 [J], where C = capacitance [F] and V = voltage [V] - Not variable for large-scale energy storage due to capacity and cost factors.

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Lecture 4: Working fluids Equation of state: property 1 = f(property 2, property 3) e.g. T = f(p, V) or h = f(p, T) Types of working fluids: - Air (in gas turbines, internal combustion engines, etc) - Gases such as CO2, N2, CO, CH4 (in exhaust products or as fuels) - Water (in steam turbines) - Refrigerants (in refrigerators, air-conditioners, heat pumps) These working fluids can conveniently be split into two categories: 1. Ideal (perfect) gases 2. Condensable gases (water/steam and refrigerants) 1. Ideal Gases Two laws for all gases at low density: 1. At constant temp., pV = constant  (Boyle’s Law) 2. Adiabatic throttling causes no temperature change (Joule-Kelvin experiment) From these observations, we have the ideal gas law:

pV = nR0 T  p - pressure V - volume

n - number of moles of gas present T - temp. in K R0  - universal gas constant = 8.314 kJ/K mol

By convention: lowercase v - specific volume m - mass of the gas R - gas constant (dependent on gas considered) R relates to the universal gas constant (R0) according to: where M is the molecular weight of the gas Ratio of heat capacities: Value of heat capacity can depend on how a process is performed. The ratio of heat capacities constant at p (cp) and v (cv) is used to predict the fluid properties. Properties of ideal gases: - For monatomic gases (He, Hg, Xe), γ = 5/3 - For diatomic gases (H2, O2, N2, air), γ = 7/3 - For polyatomic gases γ is 4/3 or less When γ, cp, cv are constant with temperature the gas is ‘fully perfect’. When γ, cp, cv are f(T), the gas is said to be ‘semi-perfect’. Enthalpy: Is a  thermodynamic quantity equivalent to the total heat content of a system. It is equal to the internal energy of the system plus the product of pressure and volume. 10

u, p and v are properties of state, so we can combine them to make a new property of state. -

This property is called enthalpy:

H = U + pV

Specific enthalpy (enthalpy per unit mass) is used for some purposes:

h = u + pv

Relating enthalpy / internal energy to temperature for ideal gases:

For most gases at normal/low temps., experiments show u is proportional to T, with progressively more deviation at higher temp. 2.Condensable Gases Non-perfect systems: The theoretical behaviour of perfect gases depends on two main assumptions: 1. Molecules behave perfectly elastically 2. Forces between the molecules are significant When the molecules become so closely packed that they are near the liquid state, the assumptions no longer apply. Non-simple systems: Not possible to deduce the shape of lines of constant temperature (isotherms) on a pV plot. Three variables are needed to specify the state of the system, i.e. to apply the equation of state Therefore the system is not simple.

e.g. heating a pot of water Alternative view: An alternative view of the surface is given by constant v lines on a p-T graph:

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Determining properties: Properties at f on the liquid saturation line are given in the tables as hf, sf, etc. and properties of g on the vapour saturation line are given as hg etc. How do we find properties at point A, say? We use the dryness fraction

Dryness fraction: It is denoted by x  and is the mass fraction of the substance that is in the g state. x  is 0 at f and is 1 at g. Thus,

and similarly for other properties e.g. 1: if h is known and x is required

e.g. 2: if x is known and h is required

Using tables for superheated steam Steam tables: These typically give u, v, h and another property, entropy, for any particular combination of pressure and temperature. It is assumed that between the adjoining sets of points given in the tables, the variation of the properties is linear.  Linear interpolation: used if the values of interest lie between two given sets of conditions. - If the value of h at T is required, and T is between given conditions T1 and T2, then:

solve for h:

The inverse of the process is to find the temperature when the enthalpy is known. The equation solved for T is:

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Multiple interpolations: the technique is to perform three linear interpolations. The first two determine the enthalpy at the desired pressure and the final uses these two to find the enthalpy at the correct temperature and pressure. h 11  , h 12  , h 21  , h22   are known from tables

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Interpolate at T 1  to get h 1  at desired p. Interpolate at T 2  to get h 2  at desired p.

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Now interpolate between T 1  and T2  for pressure p  to get enthalpy at (p, T).

Using tables for saturated water and steam Saturated water and steam: (properties on pages 2 to 5 of tables). - Saturated liquid properties are denoted by subscript: f - Saturated vapour properties denoted by subscript: g - Difference between saturated liquid and vapour: fg pg2:

pg3:

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pg5:

(bottom of pg5)

PROBLEM SET 2 COVERED UP TO HERE

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Lecture 5: Heat transfer: conduction, convection and radiation The main mechanisms for heat transfer are: conduction, convection and radiation.

1.Heat transfer by conduction Fourier rate law for conduction: Conduction: transfer of heat energy via molecular vibration. Heat flux can be expressed by a linear law known as Fourier rate equation. - minus sign ensures heat flow from hot to cold - the dot on top of the Q means it has been differentiated once against time Qn - heat flux [W] k - thermal conductivity [W m-1  K-1  ] A - cross-sectional area normal to heat flux direction (n) T - temperature [K] dT/dn - rate of change of temperature w/ respect to position Thermal conductivity: It quantifies the ability of a material to conduct heat It varies widely for different materials (more or less 5 orders of magnitude) The values for some materials are listed in the Data Book Conductivity is assumed not to change with temperature. Conduction through: - A slab: Heat flux is the same at any x , and so:

and therefore:

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Composite (more than one layer of material) slab: (consider unit area - A=1m2 ) Heat flux is the same at any x , divide by A to get to heat flux per unit area

Therefore:

The ‘d/k’ terms are “thermal resistances [m2 K W-1  ] analogous to electrical resistance in series. In this case we have three in series:

Boundary conditions (contact resistance): Thermal contact resistance causes the temperature profile through a composite medium (in practice) to show a sudden drop across the interface between the adjoining materials. Need to take into account what is going on on the interfaces. - This is treated as a simple discontinuity (step) - It is actually a result of the structure of the interface When considering this for calculations, contact resistance is assumed to be negligible.

2.Heat transfer by convection Heat transfer coefficient: We do not always know the external temperature of a simple or composite slab. Very often the external surface is in contact with a fluid, and transfers heat to it by convection. Convection: h  eat flow by a combination of mass transfer and conduction. It is the movement caused within a fluid by the tendency of hotter and therefore less dense material to rise, and colder, denser material to sink under the influence of gravity, which consequently results in transfer of heat. Two types of convection: - Forced convection: the fluid is pumped or blown past the surface, and we need to know the fluid flow pattern to predict the heat transfer (e.g. air conditioner, car radiator, etc). - Natural convection: the fluid motion is only driven by the buoyancy* effects created by the density differences between hot and cold fluid. *Buoyancy: force exerted on an object that is wholly or partly immersed in a fluid.

We treat convection as a “thermal resistance”. Heat transfer coefficient (h ) : used to quantify convection

Q - heat flow [W] h - heat transfer coefficient [W m-2 K-1] - h  is not enthalpy in this context A - Heat transfer area [m2] ΔT - temperature difference Composite slab with fluid boundaries: e.g. heat flow through the wall of a house or in a heat exchanger. Heat flow per unit area through each layer is the same;

Therefore:

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The terms in...