Thermodynamics is the study of energy and its transformations. It helps predict the feasibility and extent of chemical reactions based on temperature and pressure conditions. A system exchanges energy and matter with its surroundings. Thermodynamic processes include isothermal, isochoric, isobaric, and adiabatic processes. The first law of thermodynamics states that energy is conserved and the change in internal energy of a system equals heat supplied plus work done. Enthalpy is a state function that is the sum of a system's internal energy and pressure-volume work, and its change is a measure of heat absorbed or released at constant pressure.
1) The document presents information on ordinary differential equations including definitions, types, order, degree, and solution methods.
2) Differential equations can be written in derivative, differential, and differential operator forms. Common solution methods covered are variable separable, homogeneous, linear, and exact differential equations.
3) Applications of differential equations include physics, astronomy, meteorology, chemistry, biology, ecology, and economics for modeling various real-world systems.
This document discusses power series solutions and the Frobenius method for solving ordinary differential equations with variable coefficients. It explains that power series can be used to find solutions around ordinary points, while the Frobenius method extends this approach to regular singular points through generalized power series involving an index term. The Frobenius method involves making an ansatz for the solution as a power series with an unknown index, then determining the index and coefficients by substituting into the differential equation and setting terms of different powers of x equal to zero.
This document discusses quantification in logic. Quantification transforms a propositional function into a proposition by expressing the extent to which a predicate is true. There are two main types of quantification: universal quantification and existential quantification. Universal quantification expresses that a predicate is true for every element, while existential quantification expresses that a predicate is true for at least one element. The document provides examples and pros and cons of each type of quantification and notes that quantification operators like ∀ and ∃ take precedence over logical operators.
The document discusses applications of differential equations. It begins by providing a brief history of differential equations, noting they were independently invented by Newton and Leibniz. It then defines ordinary and partial differential equations. Examples of applications are given for modeling phenomena like cooling, oscillations, and game development. Specific differential equations like Laplace's, heat, and wave equations are discussed along with physical applications in fields like physics, engineering, and biology. Newton's law of cooling is provided as a motivating example and its applications are outlined.
This document defines and provides examples of linear differential equations. It discusses:
1) Linear differential equations can be written in the form P(x)y'=Q(x) or P(y)x'=Q(y), where multiplying both sides by an integrating factor μ results in a total derivative.
2) First order linear differential equations of the form P(x)y'=Q(x) have an integrating factor of e∫P(x)dx. The general solution is y(IF)=C.
3) Bernoulli's equation is a differential equation of the form P(x)y'+Q(x)y^n=R(x), where the general solution depends
In which i describe all the features of decoder. All the functionalities describe with the circuits and truth tables. So download and learn more about decoder. Decoder Full Presentation.
APPLICATION OF HIGHER ORDER DIFFERENTIAL EQUATIONSAYESHA JAVED
1) The document discusses modeling and applications of second order differential equations. It provides examples of second order differential equations that model vibrating springs and electric current circuits.
2) Solving second order differential equations involves finding the complementary function and particular integral. The type of roots in the auxiliary equation determines the form of the complementary function.
3) An example solves a second order differential equation modeling a vibrating spring to find the position of a mass attached to the spring at any time.
The document defines the normal or canonical form of a matrix. It states that a matrix A of order mxn is in normal form if it can be reduced to the form [I|0] using elementary transformations, where I is the rxr identity matrix and r is the rank of the matrix. The normal form partitions the matrix into blocks with the identity matrix I containing the pivot positions and zeros elsewhere.
1) The document presents information on ordinary differential equations including definitions, types, order, degree, and solution methods.
2) Differential equations can be written in derivative, differential, and differential operator forms. Common solution methods covered are variable separable, homogeneous, linear, and exact differential equations.
3) Applications of differential equations include physics, astronomy, meteorology, chemistry, biology, ecology, and economics for modeling various real-world systems.
This document discusses power series solutions and the Frobenius method for solving ordinary differential equations with variable coefficients. It explains that power series can be used to find solutions around ordinary points, while the Frobenius method extends this approach to regular singular points through generalized power series involving an index term. The Frobenius method involves making an ansatz for the solution as a power series with an unknown index, then determining the index and coefficients by substituting into the differential equation and setting terms of different powers of x equal to zero.
This document discusses quantification in logic. Quantification transforms a propositional function into a proposition by expressing the extent to which a predicate is true. There are two main types of quantification: universal quantification and existential quantification. Universal quantification expresses that a predicate is true for every element, while existential quantification expresses that a predicate is true for at least one element. The document provides examples and pros and cons of each type of quantification and notes that quantification operators like ∀ and ∃ take precedence over logical operators.
The document discusses applications of differential equations. It begins by providing a brief history of differential equations, noting they were independently invented by Newton and Leibniz. It then defines ordinary and partial differential equations. Examples of applications are given for modeling phenomena like cooling, oscillations, and game development. Specific differential equations like Laplace's, heat, and wave equations are discussed along with physical applications in fields like physics, engineering, and biology. Newton's law of cooling is provided as a motivating example and its applications are outlined.
This document defines and provides examples of linear differential equations. It discusses:
1) Linear differential equations can be written in the form P(x)y'=Q(x) or P(y)x'=Q(y), where multiplying both sides by an integrating factor μ results in a total derivative.
2) First order linear differential equations of the form P(x)y'=Q(x) have an integrating factor of e∫P(x)dx. The general solution is y(IF)=C.
3) Bernoulli's equation is a differential equation of the form P(x)y'+Q(x)y^n=R(x), where the general solution depends
In which i describe all the features of decoder. All the functionalities describe with the circuits and truth tables. So download and learn more about decoder. Decoder Full Presentation.
APPLICATION OF HIGHER ORDER DIFFERENTIAL EQUATIONSAYESHA JAVED
1) The document discusses modeling and applications of second order differential equations. It provides examples of second order differential equations that model vibrating springs and electric current circuits.
2) Solving second order differential equations involves finding the complementary function and particular integral. The type of roots in the auxiliary equation determines the form of the complementary function.
3) An example solves a second order differential equation modeling a vibrating spring to find the position of a mass attached to the spring at any time.
The document defines the normal or canonical form of a matrix. It states that a matrix A of order mxn is in normal form if it can be reduced to the form [I|0] using elementary transformations, where I is the rxr identity matrix and r is the rank of the matrix. The normal form partitions the matrix into blocks with the identity matrix I containing the pivot positions and zeros elsewhere.
This presentation gives the basic idea about the methods of solving ODEs
The methods like variation of parameters, undetermined coefficient method, 1/f(D) method, Particular integral and complimentary functions of an ODE
Linear differential equation with constant coefficientSanjay Singh
The document discusses linear differential equations with constant coefficients. It defines the order, auxiliary equation, complementary function, particular integral and general solution. It provides examples of determining the complementary function and particular integral for different types of linear differential equations. It also discusses Legendre's linear equations, Cauchy-Euler equations, and solving simultaneous linear differential equations.
Partial differential equation & its application.isratzerin6
Partial differential equations (PDEs) involve partial derivatives of dependent variables with respect to more than one independent variable. PDEs can be linear if the dependent variable and all its partial derivatives occur linearly, or non-linear. PDEs are used to model systems in fields like physics, engineering, and quantum mechanics, with examples being the Laplace, heat, and wave equations used in fluid dynamics, heat transfer, and quantum mechanics respectively. The heat equation specifically describes the distribution of heat over time in a given region.
this is the ppt on application of integrals, which includes-area between the two curves , volume by slicing , disk method , washer method, and volume by cylindrical shells,.
this is made by dhrumil patel and harshid panchal.
This chapter discusses differentiation, including:
- Defining the derivative using the limit definition of the slope of a tangent line.
- Basic differentiation rules for constants, polynomials, sums and differences.
- Interpreting the derivative as an instantaneous rate of change.
- Applying the product rule and quotient rule to differentiate products and quotients.
- Using differentiation to find equations of tangent lines, velocities, marginal costs, and other rates of change.
This document provides examples and explanations of double integrals. It defines a double integral as integrating a function f(x,y) over a region R in the xy-plane. It then gives three key points:
1) To evaluate a double integral, integrate the inner integral first treating the other variable as a constant, then integrate the outer integral.
2) The easiest regions to integrate over are rectangles, as the limits of integration will all be constants.
3) For non-rectangular regions, the limits of integration may be variable, requiring more careful analysis to determine the limits for each integral.
The document discusses the Gauss Divergence Theorem, which states that the volume integral of the divergence of a vector field over a volume is equal to the surface integral of that vector field over the bounding surface of the volume. The divergence of a vector field at a point represents the flux of that vector field diverging out per unit volume at that point. The divergence can be positive, negative, or zero, indicating whether there are sources, sinks, or neither of the vector field at that point.
First order linear differential equationNofal Umair
1. A differential equation relates an unknown function and its derivatives, and can be ordinary (involving one variable) or partial (involving partial derivatives).
2. Linear differential equations have dependent variables and derivatives that are of degree one, and coefficients that do not depend on the dependent variable.
3. Common methods for solving first-order linear differential equations include separation of variables, homogeneous equations, and exact equations.
This document explains Simpson's 1/3rd rule for numerical integration. Simpson's 1/3rd rule approximates the integral of a function over an interval by breaking the interval into equal subintervals and approximating the function within each subinterval as a quadratic polynomial. The approximation takes the function values at the endpoints and midpoint of each subinterval. The approximations over all subintervals are then summed to give an approximation of the full integral. Important considerations for applying Simpson's 1/3rd rule include using an even number of equal subintervals and having a minimum of 3 points defined in each subinterval.
Newton's forward and backward interpolation are methods for estimating the value of a function between known data points. Newton's forward interpolation uses a formula to calculate successive differences between the y-values of known x-values to estimate y-values for unknown x-values greater than the last known x-value. Newton's backward interpolation similarly uses differences but to estimate y-values for unknown x-values less than the first known x-value. The document provides an example of using Newton's forward formula to find the estimated y-value of 0.5 given a table of x and y pairs, calculating the differences and plugging into the formula. It also works through an example of Newton's backward interpolation to estimate the y-value at
1. The document defines ordinary and partial differential equations and discusses the order and degree of differential equations.
2. Examples of common second order linear differential equations with constant coefficients are given, including equations for free fall, spring displacement, and RLC circuits.
3. The document also discusses homogeneous linear equations and Newton's law of cooling as examples of differential equations.
The document discusses various methods to compute the rank of a matrix:
1) Using Gauss elimination, where the rank is the number of pivot columns in the echelon form of the matrix.
2) Using determinants of sub-matrices (minors), where the rank is the largest order of a non-zero minor.
3) Transforming the matrix to normal form using row and column operations, where the rank is the number of non-zero rows of the resulting identity matrix.
Worked examples are provided to illustrate computing the rank of matrices using these different methods.
In this presentation we will learn Del operator, Gradient of scalar function , Directional Derivative, Divergence of vector function, Curl of a vector function and after that solved some example related to above.
Gradient in math
Directional derivative in math
Divergence in math
Curl in math
Gradient , Directional Derivative , Divergence , Curl in mathematics
Gradient , Directional Derivative , Divergence , Curl in math
Gradient , Directional Derivative , Divergence , Curl
This document discusses the divergence of a vector field and the divergence theorem. It begins by defining the divergence of a vector field as a measure of how much that field diverges from a given point. It then illustrates the divergence of a vector field can be positive, negative, or zero at a point. The document expresses the divergence in Cartesian, cylindrical, and spherical coordinate systems. It proves the divergence theorem, which states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence of the field over the enclosed volume. The document provides two examples applying the divergence theorem to calculate outward fluxes.
This document provides an introduction to ordinary differential equations (ODEs). It defines ODEs as differential equations containing functions of one independent variable and its derivatives. The document discusses some key concepts related to ODEs including order, degree, and different types of ODEs such as variable separable, homogeneous, exact, linear, and Bernoulli's equations. Examples of each type of ODE are provided along with the general methods for solving each type.
This document summarizes key concepts about polynomials:
1) It defines a polynomial as an algebraic expression involving variables and their powers, and defines the degree of a polynomial as the highest power of the variable.
2) It describes different types of polynomials based on degree, including constant, linear, quadratic, cubic, and biquadratic polynomials.
3) It explains that a zero of a polynomial is a value that makes the polynomial equal to zero when substituted for the variable, and discusses the relationship between zeros and coefficients of polynomials.
- A differential equation involves an independent variable, dependent variable, and derivatives of the dependent variable with respect to the independent variable.
- The order of a differential equation is the order of the highest derivative, and the degree is the exponent of the highest order derivative.
- Linear differential equations involve the dependent variable and its derivatives only to the first power. Non-linear equations do not meet this criterion.
- The general solution of a differential equation contains as many arbitrary constants as the order of the equation. A particular solution results from assigning values to the arbitrary constants.
- Differential equations can be solved through methods like variable separation, inspection of reducible forms, and finding homogeneous or linear representations.
The document discusses the concept of the rank of a matrix. The rank of a matrix is defined as the maximum number of linearly independent rows or columns. There are two methods to determine the rank: determinant methods and elementary row/column reduction methods. Determinant methods find the largest non-zero minor of a matrix, and the order of that minor is the rank. The rank is always less than or equal to the number of rows or columns.
This document provides an introduction to chemical thermodynamics and key concepts. It discusses different forms of energy including kinetic, potential, heat, mechanical, electrical, and chemical energy. Thermodynamics is defined as the branch of science dealing with different energy forms and changes in physical and chemical processes. The document outlines the scope and limitations of thermodynamics and introduces basic concepts like system, surroundings, boundary, open system, closed system, isolated system, extensive and intensive properties, state and state functions, and types of processes including isothermal, isobaric, isochoric, and adiabatic. It also discusses thermodynamic equilibrium, nature of work and heat, reversible processes, and the expression for maximum work in an
System and its types, chemical thermodynamics, thermodynamics, first law of thermodynamics, enthalpy, internal energy, standard enthalpy of combustion, formation, atomization, phase transition, ionization, solution and dilution,second law of thermodynamics, gibbs energy change, spontaneous and non-spontaneous process, third law of thermodynamics
This presentation gives the basic idea about the methods of solving ODEs
The methods like variation of parameters, undetermined coefficient method, 1/f(D) method, Particular integral and complimentary functions of an ODE
Linear differential equation with constant coefficientSanjay Singh
The document discusses linear differential equations with constant coefficients. It defines the order, auxiliary equation, complementary function, particular integral and general solution. It provides examples of determining the complementary function and particular integral for different types of linear differential equations. It also discusses Legendre's linear equations, Cauchy-Euler equations, and solving simultaneous linear differential equations.
Partial differential equation & its application.isratzerin6
Partial differential equations (PDEs) involve partial derivatives of dependent variables with respect to more than one independent variable. PDEs can be linear if the dependent variable and all its partial derivatives occur linearly, or non-linear. PDEs are used to model systems in fields like physics, engineering, and quantum mechanics, with examples being the Laplace, heat, and wave equations used in fluid dynamics, heat transfer, and quantum mechanics respectively. The heat equation specifically describes the distribution of heat over time in a given region.
this is the ppt on application of integrals, which includes-area between the two curves , volume by slicing , disk method , washer method, and volume by cylindrical shells,.
this is made by dhrumil patel and harshid panchal.
This chapter discusses differentiation, including:
- Defining the derivative using the limit definition of the slope of a tangent line.
- Basic differentiation rules for constants, polynomials, sums and differences.
- Interpreting the derivative as an instantaneous rate of change.
- Applying the product rule and quotient rule to differentiate products and quotients.
- Using differentiation to find equations of tangent lines, velocities, marginal costs, and other rates of change.
This document provides examples and explanations of double integrals. It defines a double integral as integrating a function f(x,y) over a region R in the xy-plane. It then gives three key points:
1) To evaluate a double integral, integrate the inner integral first treating the other variable as a constant, then integrate the outer integral.
2) The easiest regions to integrate over are rectangles, as the limits of integration will all be constants.
3) For non-rectangular regions, the limits of integration may be variable, requiring more careful analysis to determine the limits for each integral.
The document discusses the Gauss Divergence Theorem, which states that the volume integral of the divergence of a vector field over a volume is equal to the surface integral of that vector field over the bounding surface of the volume. The divergence of a vector field at a point represents the flux of that vector field diverging out per unit volume at that point. The divergence can be positive, negative, or zero, indicating whether there are sources, sinks, or neither of the vector field at that point.
First order linear differential equationNofal Umair
1. A differential equation relates an unknown function and its derivatives, and can be ordinary (involving one variable) or partial (involving partial derivatives).
2. Linear differential equations have dependent variables and derivatives that are of degree one, and coefficients that do not depend on the dependent variable.
3. Common methods for solving first-order linear differential equations include separation of variables, homogeneous equations, and exact equations.
This document explains Simpson's 1/3rd rule for numerical integration. Simpson's 1/3rd rule approximates the integral of a function over an interval by breaking the interval into equal subintervals and approximating the function within each subinterval as a quadratic polynomial. The approximation takes the function values at the endpoints and midpoint of each subinterval. The approximations over all subintervals are then summed to give an approximation of the full integral. Important considerations for applying Simpson's 1/3rd rule include using an even number of equal subintervals and having a minimum of 3 points defined in each subinterval.
Newton's forward and backward interpolation are methods for estimating the value of a function between known data points. Newton's forward interpolation uses a formula to calculate successive differences between the y-values of known x-values to estimate y-values for unknown x-values greater than the last known x-value. Newton's backward interpolation similarly uses differences but to estimate y-values for unknown x-values less than the first known x-value. The document provides an example of using Newton's forward formula to find the estimated y-value of 0.5 given a table of x and y pairs, calculating the differences and plugging into the formula. It also works through an example of Newton's backward interpolation to estimate the y-value at
1. The document defines ordinary and partial differential equations and discusses the order and degree of differential equations.
2. Examples of common second order linear differential equations with constant coefficients are given, including equations for free fall, spring displacement, and RLC circuits.
3. The document also discusses homogeneous linear equations and Newton's law of cooling as examples of differential equations.
The document discusses various methods to compute the rank of a matrix:
1) Using Gauss elimination, where the rank is the number of pivot columns in the echelon form of the matrix.
2) Using determinants of sub-matrices (minors), where the rank is the largest order of a non-zero minor.
3) Transforming the matrix to normal form using row and column operations, where the rank is the number of non-zero rows of the resulting identity matrix.
Worked examples are provided to illustrate computing the rank of matrices using these different methods.
In this presentation we will learn Del operator, Gradient of scalar function , Directional Derivative, Divergence of vector function, Curl of a vector function and after that solved some example related to above.
Gradient in math
Directional derivative in math
Divergence in math
Curl in math
Gradient , Directional Derivative , Divergence , Curl in mathematics
Gradient , Directional Derivative , Divergence , Curl in math
Gradient , Directional Derivative , Divergence , Curl
This document discusses the divergence of a vector field and the divergence theorem. It begins by defining the divergence of a vector field as a measure of how much that field diverges from a given point. It then illustrates the divergence of a vector field can be positive, negative, or zero at a point. The document expresses the divergence in Cartesian, cylindrical, and spherical coordinate systems. It proves the divergence theorem, which states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence of the field over the enclosed volume. The document provides two examples applying the divergence theorem to calculate outward fluxes.
This document provides an introduction to ordinary differential equations (ODEs). It defines ODEs as differential equations containing functions of one independent variable and its derivatives. The document discusses some key concepts related to ODEs including order, degree, and different types of ODEs such as variable separable, homogeneous, exact, linear, and Bernoulli's equations. Examples of each type of ODE are provided along with the general methods for solving each type.
This document summarizes key concepts about polynomials:
1) It defines a polynomial as an algebraic expression involving variables and their powers, and defines the degree of a polynomial as the highest power of the variable.
2) It describes different types of polynomials based on degree, including constant, linear, quadratic, cubic, and biquadratic polynomials.
3) It explains that a zero of a polynomial is a value that makes the polynomial equal to zero when substituted for the variable, and discusses the relationship between zeros and coefficients of polynomials.
- A differential equation involves an independent variable, dependent variable, and derivatives of the dependent variable with respect to the independent variable.
- The order of a differential equation is the order of the highest derivative, and the degree is the exponent of the highest order derivative.
- Linear differential equations involve the dependent variable and its derivatives only to the first power. Non-linear equations do not meet this criterion.
- The general solution of a differential equation contains as many arbitrary constants as the order of the equation. A particular solution results from assigning values to the arbitrary constants.
- Differential equations can be solved through methods like variable separation, inspection of reducible forms, and finding homogeneous or linear representations.
The document discusses the concept of the rank of a matrix. The rank of a matrix is defined as the maximum number of linearly independent rows or columns. There are two methods to determine the rank: determinant methods and elementary row/column reduction methods. Determinant methods find the largest non-zero minor of a matrix, and the order of that minor is the rank. The rank is always less than or equal to the number of rows or columns.
This document provides an introduction to chemical thermodynamics and key concepts. It discusses different forms of energy including kinetic, potential, heat, mechanical, electrical, and chemical energy. Thermodynamics is defined as the branch of science dealing with different energy forms and changes in physical and chemical processes. The document outlines the scope and limitations of thermodynamics and introduces basic concepts like system, surroundings, boundary, open system, closed system, isolated system, extensive and intensive properties, state and state functions, and types of processes including isothermal, isobaric, isochoric, and adiabatic. It also discusses thermodynamic equilibrium, nature of work and heat, reversible processes, and the expression for maximum work in an
System and its types, chemical thermodynamics, thermodynamics, first law of thermodynamics, enthalpy, internal energy, standard enthalpy of combustion, formation, atomization, phase transition, ionization, solution and dilution,second law of thermodynamics, gibbs energy change, spontaneous and non-spontaneous process, third law of thermodynamics
Basic Terminology,Heat, energy and work, Internal Energy (E or U),First Law of Thermodynamics, Enthalpy,Molar heat capacity, Heat capacity,Specific heat capacity,Enthalpies of Reactions,Hess’s Law of constant heat summation,Born–Haber Cycle,Lattice energy,Second law of thermodynamics, Gibbs free energy(ΔG),Bond Energies,Efficiency of a heat engine
Thermodynamics deals with energy changes in chemical reactions and their feasibility. It describes three types of systems - open, closed, and isolated - based on their ability to exchange energy and matter with surroundings. The first law of thermodynamics states that energy in an isolated system is constant and can neither be created nor destroyed. It is expressed as a change in internal energy (ΔU) of the system equals heat (q) absorbed plus work (w) done. Entropy is a measure of randomness or disorder in a system, which typically increases for spontaneous processes that are irreversible without external influence.
1. The document discusses concepts from engineering chemistry including the laws of thermodynamics, kinetics, and related topics.
2. It explains key thermodynamic concepts such as state functions, path functions, the four laws of thermodynamics, entropy, enthalpy, and Gibbs free energy.
3. The document also discusses kinetic concepts such as activation energy, the Arrhenius equation, and enzyme catalysis using the Michaelis-Menten mechanism.
1. The document discusses concepts from engineering chemistry including the first law of thermodynamics and its applications.
2. Key topics covered include state functions, path functions, different types of processes (isothermal, adiabatic, isobaric, isochoric), work, heat, internal energy, enthalpy, and heat capacity.
3. Examples are provided to demonstrate how to use the first law of thermodynamics to calculate work, heat, and changes in internal energy and enthalpy for various thermodynamic processes including isothermal expansion of gases.
Heat and thermodynamics - Preliminary / Dr. Mathivanan VelumaniMathivanan Velumani
The document discusses key concepts in thermodynamics including:
1. Thermodynamic states are characterized by macroscopic properties like temperature, pressure, and volume that determine a system's internal state and interaction with external bodies.
2. Thermal equilibrium exists when temperature is uniform throughout a system, as stated by the zeroth law of thermodynamics.
3. Internal energy (U) is the energy associated with the random, disordered motion of molecules within a system.
The document discusses the first law of thermodynamics which states that energy cannot be created or destroyed, only changed from one form to another. It also discusses different types of thermodynamic systems and processes, including open, closed, and isolated systems, as well as isothermal, adiabatic, isobaric, and isochoric processes. Specific heat capacities at constant volume and pressure are also defined for gases on both a specific and molar basis.
This document discusses key concepts in thermodynamics including:
1. It defines thermodynamics as dealing with energy changes in chemical reactions and their feasibility.
2. It describes open, closed, and isolated systems and different types of processes like isothermal, isobaric, isochoric, and adiabatic processes.
3. It explains important thermodynamic properties and concepts such as internal energy, enthalpy, Gibbs free energy, entropy, and the three laws of thermodynamics.
process, Thermodynamic process,workdone, relation between pressure volume,first law of thermodynamic,need of second law,statement of second law,carnot heat engine,efficiency,numericals
A homogeneous thermodynamic system is one whose properties are uniform throughout. A heterogeneous system contains distinct phases.
There are several types of thermodynamic processes including isochoric (constant volume), isobaric (constant pressure), and adiabatic (no heat transfer). Extensive properties depend on amount of substance and intensive properties do not.
The first law of thermodynamics states that energy is conserved and heat and work are equivalent. For an ideal gas undergoing an adiabatic process, PVγ is constant, where γ is the heat capacity ratio.
This document defines key concepts in thermodynamics over 16 pages. It discusses systems and boundaries, open and closed systems, different types of processes like isothermal and adiabatic processes. It also defines properties of pure substances like saturated liquid and vapor. The first law of thermodynamics is explained as well as concepts like heat, work, internal energy. Devices like nozzles, diffusers, turbines and compressors are covered. The document also discusses entropy, the Carnot heat engine principle, and efficiency of compressors and turbines.
Chemical Thermodynamics - power point new.pptxWill
1. The document discusses various thermodynamic concepts including system, surroundings, universe, open system, closed system, isolated system, extensive and intensive properties, state functions, path functions, thermal equilibrium, chemical equilibrium, mechanical equilibrium, and different types of thermodynamic processes.
2. Key thermodynamic processes discussed are isothermal, adiabatic, isochoric, and isobaric processes. Equations are derived for work done during these processes.
3. The document also covers the first law of thermodynamics, enthalpy, exothermic and endothermic reactions, and relationships between heat, work and internal energy change for different processes.
1st Lecture on Chemical Thermodynamics | Chemistry Part I | 12th StdAnsari Usama
This document discusses key concepts in chemical thermodynamics including:
1. Thermodynamics deals with energy changes during physical and chemical transformations. It defines systems, surroundings, and different types of systems.
2. Properties of systems are either extensive (depend on amount of matter) or intensive (independent of amount of matter). State functions depend on the state of the system but not the path.
3. Processes can be isothermal, isobaric, isochoric, adiabatic, or reversible. Maximum work occurs during a reversible, isothermal expansion against a gradually decreasing external pressure.
This document provides an overview of key concepts in thermodynamics, including:
- The 0th law defines temperature and thermal equilibrium.
- The 1st law concerns the conservation of energy and defines internal energy. Energy cannot be created or destroyed, only changed in form.
- The 2nd law defines entropy and the direction of spontaneous processes over time. Entropy always increases over time for isolated systems.
- An equation of state relates the state variables like pressure, volume, and temperature that define the state of a system at equilibrium.
The document discusses various thermodynamic concepts including:
1) Reversible and irreversible processes, with reversible processes proceeding in both directions and irreversible only proceeding in one direction.
2) Extensive and intensive properties, with extensive depending on amount and intensive independent of amount.
3) Types of processes like isothermal, isobaric, isochoric, cyclic, and adiabatic classified based on constant temperature, pressure, volume, state functions, and no heat transfer.
4) First law of thermodynamics stating energy is conserved and can be converted between forms.
5) Free energy and how it relates to available work for a system.
Thermodynamics is the study of energy relationships involving heat, work, and transfers between systems and surroundings. A system refers to the part being studied, while the surroundings are all else. Systems can be open, allowing transfers with surroundings, closed, allowing only energy transfers, or isolated, with no transfers. The state of a system is described by measurable properties like pressure, volume, and temperature. Internal energy and enthalpy are state functions that depend on these properties. The first law of thermodynamics states that energy is conserved in transfers between systems and surroundings as either heat or work.
thermodynamics, basic definitions with explanations, heat transfer, mode of heat transfer, Difference between thermodynamics and heat transfer?What is entropy?
1. Chemical thermodynamics deals with energy changes that occur during chemical reactions and processes involving chemical substances.
2. It helps determine the feasibility and extent of chemical reactions and processes under given conditions based on fundamental laws of physical chemistry.
3. Key concepts include the various types of systems (open, closed, isolated), state functions, state variables, and different thermodynamic processes (isothermal, adiabatic, isobaric, isochoric).
Similar to Thermodynamics Part 1 by Shobhit Nirwan.pdf (20)
This document provides an overview of solid state chemistry. It defines solids as matter with a definite shape and volume, where the constituent particles possess fixed positions and can only oscillate. Solids are classified as crystalline or amorphous based on the ordering of particles. Crystalline solids have long-range order while amorphous solids only have short-range order. Important properties of solids discussed include density, rigidity, melting points, and electrical conductivity. The document also describes different types of crystalline solids based on bonding - ionic, molecular, metallic, and covalent network solids. Unit cell structure, crystal systems, and packing efficiency of particles in cubic unit cells are also summarized.
Chemistry (Module 1) introduces several key concepts:
[1] It discusses units and dimensions, and defines the seven SI base units - meter, kilogram, second, kelvin, ampere, candela, and mole.
[2] It explains prefixes that are used to modify the SI units and increase or decrease their magnitude, such as milli, centi, kilo, mega.
[3] It describes derived units which are derived by combining the basic units through multiplication or division, such as m3 for volume, m2 for area, and J for energy.
[4] It discusses the classification of matter as elements, compounds, and mixtures based on their chemical
This document provides an overview of English verb tenses, including simple, continuous/progressive, perfect, and perfect continuous forms. For each tense (present, past, future), it lists the basic formula using either the simple form of the verb, a present participle ("verb+ing") or past participle ("third form"). Examples are also given for each tense using the verbs "write" and "give". Two blank worksheets are included for practicing forming sentences in different tenses.
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2. ①
Thermodynamics is the study of different forms of energy and their interconversion
and flow of energy.
Thermodynamics helps in :
→
predicting feasibility of a reaction ,
ie.
whether certain reaction is possible under
given conditions of temperature and pressure or not .
→
predicting the extent of chemical reaction.
→
predicting the force that drives chemical (reaction) process.
# SOME IMPORTANT TERMINOLOGIES :-
system , surroundings and Boundry
system -
Spetic part of universe that is studied by us for study of energy
changes.
Surroundings.
Everything that is external to system
Boundary -
something that separate system from
surroundings.
System +
Surroundings=
Universe
(based on
exchange of energy 4 matter
System with surroundings)
X N Y
OPEN SYSTEM CLOSED SYSTEM ISOLATED SYSTEM
→
Energy V (Beto) →
Energy VIDEto) →
Energy X He-0
)
→
matter V
(Beto
) -
Matter X (Dm
-
- o
) - Matter X (Dm-0
)
state of the system -
condition in which system is present. State can be known
by known some specific properties of the system. for ex :-
In case of ideal
gas
-
IPN, T) are state variables .
State function Any property of the system which is dependent only on the state
of system and not on the way that state has been achieved.
For
Igor P -
Pressure H→
Enthalpy
V→ Volume S→ Entropy
T→ Temperature vs Internal energy of system
G →
gibb's free energy
⑧ Change in state function are not state function.
of DT,
DV , DG are not
state function.
Path function Quantities which are dependent on the path through which a
particular state has been achieved.
eg:
-
work,
heat,
heat capacity.
3. ②
Extensive Property Properties which are dependent on mass or size of
system . These are additive in nature.
egfr v, men ,
total heat capacity,
total internal
energy , Hg Goss .
⑦tensive
Property which are independent of mass or size of system. These
↳Independent of properties are not additive in nature.
Forego.
-
Tg Pg motor
mass.
heat capacity , sp heat capacity ,
9 ,
concentration,
colour
,
refractive index ,
molar enthalpy g viscosity, pH ,
Eo
Trick → that term tf "
molas' '
at
"
specified elf Intensive et etat 1
Thermodynamic Process There are infinite thermodynamic process out of which
following are important or
→ Isothermal Process : T-
constant i. e.
Ti -
-
Tf
00g DT=
Old7=0
→
Isochoric Process : Volume Iv) → constant
Fe .
Vi -
-
tf
08
,
DV / dV=O
→
Isobaric Process : pressure G) →
constant
Fe.
Pi=
Pf
org DP =
OldP - O
→ Adiabatic Process :
Exchange of heat between system and surroundings
-
-
O.
i.e.
Dq=0/dq=0
→
Cyclic Process : It initial and final States after a process are same ,
then
it is known as
cyclic process.
change in stateful must be zero .
→
Reversible and Irreversible processes :-
REVERSIBLE IRREVERSIBLE
L.
It takes infinite time. I . It takes finite time.
↳
(
IIHF Process tif Reversible 4¥ ed if
321ft ET Fti step FAF tf 44T ETAT theft
TENT Reversible
process ahf ehf ett
2. The system remains in thermodynamic 2. The
system does not remains in thermodynamic
equilibrium with
surroundings throughout equilibrium with
surroundings throughout
the
process. the process .
3. Practically no
process is reversible in 3.
All process in nature are Breuersible.
nature. lie. it is ideal condition)
4. ③
#
Sign convention of Heat and work :-
← a q
-
- tore
← w ⑦re
Heat or If heat is
given to system ⑦ve system
- q-
- Ove
It heat is released Ove →
we -0ve
Werk:-
It work is done on system or compression re
It work is done by system or
expansion ve
WORK
↳ Mode of transfer of energy when system and surroundings differ in
pressure ,
till the pressures become equal.
If an object is displaced through a distance doe by a force f, the amount of
work done is
given by,
W = f x da
# Mechanical work Done by a system :-
Total volume of the
gas
-
-
V
Pressure of the
gas
=P
external Pressure =
Pex
It text > P ,
the piston moves inward till the pressure of the
gas becomes equal to external pressure lie .
p=Pext)
Now this condition F- Pert can be achieved by two ways
:(
1) It Achieve in single step lie.
Irreversible Process)
final volume =
Vt
Distance moved by piston =L
cross-sectional area of piston
-
-
A
volume change CAV) = lxA (Vt-
Vi)
Now ,
we know
Petz do f =
pxA
and we know,
W-
- f xd lie.
force x distance)
=
text xAxl
=
text t-
AV)
o :
/W=-PDT or
-
Pext ( Vf -
Vi)
-
t =
C-re) sign is used for work done by the system in case of expansion in
volume by convertors .
5. ④
NERI l 2L of an ideal gas at a
pressure of 20 atm expands isothermally
against a constant external pressure of Latin ,
until its total
volume Ps LOL . How much work is done during the expansion ?
Sofi-
W= -
Peet ( Vt -
Vi)
= -
L (Lo -
2)
= -
I 18) -
8L atm
(2) If it is Achieved in Number of steps ( ie .
Reversible Process)
It pressure is not constant at each
stage of comparison and
changes in such a manner so that it is always infinitesimally
greater than the pressure of the
gas and the volume during the
process
decreases
by an infinitesimal amount dv,
then work done is given by
the expression Vt
w = -
fpexdv
Vi
Now for compression , Pex
-
pin tdv
and for expansion , per pin-
dr
o
: In
general , Pex=
(pinIdp)
ooo Wren =
(pin Idp)dir
since, dpxdv is very small in comparison to pindv ,
so
Vt
Wren= -
I pin DV
vi
As we know
? pkn RT ( for ideal
gas)
p
-
-
mfs
Wren -
=
-
fit n RT
IF =
-
n RT
lnV¥
Wrev = -
2303 nRT
log¥
Via initial Volume
Vt =
final Volume
n =
no.
of moles
R =
gas constant
T =
absolute Temperature (in K)
⑧ Woev =
Wmax ( ie .
for getting maximum work, system should do work
in reversible process).
6. ⑤
⑧ FREEEXPANS.IO# line .
Pex - O)
↳ .
: 1×1=0 ,
whether process is reversible or
HEAT irreversible .
4 If the
energy exchange takes place because of temperature difference ,
then
it is known as heat .
Specific Heat
capacity
-
The heat required to raise the temperature of one unit
mass
by L
degree (either Celsius or Kelvin). The specific heat
capacity is
denoted by Cg formula :
q= c × m × be
q= heat required to raise temperature
by Ic
and if C is the heat capacity of n mole of the c =
specific heat
capacity
system , then its molar heat capacity cm is m
-
-
mass
given by ¥4 . at =
temperature change link)
-
Heat capacity at constant volume Kv) : The amount of heat required toraise
the temperature of one mole of a
gas by one
degree, when volume of the
gas is
kept constant.
Heat capacity at constant Pressure Kp) : The amount of heat required to
raise the temperature of one mole of a
gas by one degree ,
when pressure
of the gas is kept constant .
Now we can write equation of heat q ,
at constant volume as
q =
Cvn
at constant
pressure as
qp
=
Cp DT
k⑦ Cp and Cv are related to each other
by the expression Cp-
Cr -
n R
↳ Derivation stat shaft
•
Cpt Cv (always)
•
Cpk,
Ratio is represented by 8.
# INTERNAL ENERGY (U) :
Every system is associated with a definite
amount of energy ,
called the Internal Energy of the system.
°
It is represented by V or E.
*
° It is a state function.
Iwata
°
It is an extensive property
-
④BThe absolute value of internal Energy possessed by a substance cannot
be calculated because it is not possible to predict the exact values of
different forms of energy. Thus,
we can just calculate the change in
internal energy,
which is achieved by changing state of a system.
↳ Las
7. ⑥
First law of Thermodynamics IF LOTT
°
It is based on the law of conservation of Energy.
°
According to this total energy of the universe is always conserved and only
one form of energy changes to another energy .
£,
Consider a
system in a state initially in which internal
energy is Es . If q amount of heat is givento it and W
amount of work is done on it then its total internal
energy is Ez .
.
'
.
fz= EL +
get W
Ez-
EL =
get W
T
AV or DE -
=
ft
'
W
LIK A system does 2005 work on surroundings by absorbing 250J of heat.
Calculate the
change in internal Energy.
ans:-
=
W= -2005 fusing sign-
convention
q
= t 250J
Now, by fLOT
g
DU =
Wtq
DU =
-
200+250
DE 50 J
II:-
100J of work was done on a
spring and 155 escaped to the surroundings
as heat ,
BE or AV =
? ?.
SII.
-
DU =
qtw
= -15+100
=
857
=
E:
-
It an electric motor produced 15kt of Energy each second as mechanical
work and lost 2 KJ as heat to surroundings ,
DV =
? ? .
see:
NDE ¥4772 fas YE
-
'
Ink})
-17k¥
K3B ① If Isothermal process ( ie .
At-0
)
since DT-
- O
% DU= 0
.
'
. f- LOT
0=qtWy
1q=-W_
Pf isothermal reversible, q=
-
Wren=
2.303 nRT
dogft.to)
8. ⑦
if isothermal irreversible, f-
-
Wiser =
pex(Vt-
Vi)
② If Isochoric process ( i.e .
AV-
-
O)
since DV-
-
O
: .
into f: dW= -
Pexdv)
o
: f- LOT /DU=qT
→ this q
at constant volume fire.
qv ) .
③ If A-diabetic process lie .
Bq -0
)
-
i. f- lot
lDU=W→ work done in adiabetic process.
# limitations of floe
:O
It fails to explain the direction of process .
° It fails to explain how much heat
energy
would be transferred from one
system to another.
ENTHALPY ( H)
↳ It is defined as total heat content of the system . It is equal to the sum of
internal energy and pressure
-
volume work.
° It is a state function
° It is an extensive property.
Mathematically ,
H = Ut Pv
change in Enthalpy : It is the heat absorbed or evolved by the system at
constant pressure.
CITI UIT 34kt
)
simply g
DH=9P#-
②
also
, /DH=DUtpDV
for exothermic (system loses to
surroundings) as Gpa soDHLO
similarly , for endothermic gas q 70 :.
AH >0.
K3④ 0
In ② g if Tsochoric (i -
e.
constant volume).
DH = DU
↳ Thus
,
we can say that
"
Heat supplied at constant pressure is the
measure of enthalpy change ,
while the heat supplied at constant volume is the
measure of internal energy change
"
.
here
Dng= total moles ofgaseous
o for gaseous reactions,
DH = DU t
DngRT products minus total
moles of gaseous reactants.
9. ⑧
# Proof of Xp-
Cv-
-
R)
As we know,
BH = DU t DlpV) pv
-
- n Re
DH -
but DIRT) for A-
Lg pitRT
DH = But RD T
CpDT =
CvAT -1 RAT
Cp =
Cr t R
14-4=7
-
→
Please Read calorimetry theory from NCERT.
(DV & DH measurements)
Enthalpy change , AH of a Reaction -
Reaction Enthalpy
In a chemical reaction ,
reactants are converted into products and is
represented by '
reactants →
Products
The enthalpy change accompanying a reaction is called the reaction enthalpy.
This enthalpy change of a chemical reaction ,
is
given by the symbol Dr H.
Dr H =
(sum of enthalpies of products) -
Isum of enthalpies of reactants).
org Dr H =
⇐ Xp Hp -
Yi IHR
ni, Yi stoichiometric coefficients of products and reactants
respectively in a balanced equation.
Hp Enthalpy of formation of products.
HR Enthalpy of formation of Reactants .
forty:- C
Hylglt 2021g) -
C
02cg) t 2h20 le)
Dr H =
l H (coz ,g)
-12 HItho,
e) I -
(Hetty , g) t 2 H
Koz , g) )
k3④ On
reversing a reaction , the sign of DH is also reversed but its
magnitude remains same.
# Standard Enthalpy of Reaction : the standard enthalpy of reaction
is the enthalpy change for a reaction when all the
participating
substances are in their standard States .
The purest and most stable form of a substance at L bar and at a
specified temperature is called its standard state.
10. ⑨
# Enthalpy changes during phase transformations :
conversion of solid →
liquid is
Melting .
liquid →
gas is vaporBatton.
solid →
gas is sublimation.
These processes are
collectively known as phase transformations.
(a) Enthalpy of fusion (Itu'sHQ : The enthalpy change occurring when I
mole of solid substance in its standard state melts completely into its
liquid form is called standard or molar enthalpy of fusion .
of H2O Cs) -
H2O le)
(b) Enthalpy of Vaporisatin (ArapHo) :
The enthalpy change when one mole
of a
liquid is converted into vapours at its boiling temperature and under
standard pressure CL bar) is called enthalpy of rapon'sation or molar enthalpy
of vaporis ation .
elf: H2O le) -
H2O Cg)
(c) Enthalpy of sublimation (Dsub Ho): The enthalpy change when one mole of
a lid substance sublimes (or converted into vapours) without melting at
a temperature below its
melting point land at L bar pressure) is called the
enthalpy of sublimation or molar enthalpy of sublimation .
elf's CO2 Is) tasks coz Cv)
also, Dsub HE AfusHot trap to
- .
# Standard Enthalpy of formation :
↳ The
enthalpy change accompanying the formation of one mole of a compound
from its constituent elements, when they are in their most stable States or
reference states
,
is called standard Enthalpy of formation
of
CC
graphite,Dt 2142cg) - C Hy Cg)
2C (graphite,
s) -13
High tz 02cg) - Cz
HsOHlll.A@Hzlg1g0zlg7gCCgoaphite.s
) g Brace ) ,
S (rhombic) are the most stable States or
reference States .
The standard enthalpy of formation , Dft:
of an element in its reference
slate is taken as zero.
.
⑧ Df Ho is a special case of Dott.
11. ⑧
# Hess's law of constant Heat summation :
Heat absorbed or evolved in a
given chemical reaction is same
whether the process occurs in one step or in several steps .
A D
-7
AHH TBH,
/BH=DHiDHztDt
B →C
DHz
k3B 0
Chemical reactions can be added or subtracted to get the required
equation . (if added -
enthalpy gets added
it subtracted →
enthalpy gets subtracted ).
°
If reaction is reversed,
sign of DH also reversed .
LI.
find Bff of C0cg) it:
C (
graphite) +02cg) -
coz Cg) -
A Hex -
①
coz Cg)
-
C 0cg) +
I 02cg -
D HEY .
-
②
SEI: Haaf next of allot f tf equation that tf:
.
Target equation Ccgraphite)*
I 0dg) →
CO Cg) -
⑦
7TH A tht Hf of given equations of 3of tht use htt ett
Targeted equation at
that F1
by observation,
⑦ =
② t ②
it.
AtH =
X t
Y .
Enthalpies for different types of Reactions
# Standard Enthalpy of combustion , ACH
-0
:-
The amount of heat
ev_ed# when one mole of the substance is burnt completelyin
oxygen or air ,
and all the reactants and products are in their
standard States
,
is called the standard enthalpy of combustion.
(i.e. exothermic ,
egg
: Cy tho Cg) t
Bz 02cg) - 4 Coz Capt 5th Old
°
Simply Att FA compound TT combustion that I 3¥ Oz tf React tht
CO2 and water as a
product Hita
o Our
body also
generates energy from food by the same overall process
as combustion.
12. ④
# Enthalpy of AtomBatton , Da Ho:
The enthalpy change on
breaking one mole of bonds completely to
obtain atoms in the gas phase is called the enthalpy of atomBatton.
of City Ig) →
Ccg) t 4 H Cg)
Nats) - NaCg)
# Bond Enthalpy ,
Dbond Ho :
-
As we know that energy is required
for breaking bond and for bond making , energy is released.
simply ,
Bond list tf tht energy dat etat
Bond aid Ttt energy release etat I
⑨ fomie :.
↳ Also called Bond dissociation enthalpy →
It is the enthalpy
change accompanying the breaking of one mole of covalent
bonds of a
gaseous covalent compound to give products in the
gas phase.
←symbol.
¥
→
Bond dissociation ethalpy of dihydrogen (DH-
H Hot
Hzlg) - LH Ig)
→
Clap - 2 Cdcg) -
here Ace-
ce
Ho
(b)
forpolyatomicn-oeueo.li
Also called mean Bond enthalpy .
If we take example of CHy → here all the four C-H bonds are
identical in bond
length and energy . but
they differ in
strengths
Tre.
different amount of energy is required to break each individual
bond.
So ,
in case of polyatomic molecules ,
the mean of bond dissociation
enthalpies of all bonds present in the compounds is taken.
Thus ,
in city
f , Dc-
Htt is -
I@aHIeeanwthmdsmaf.tn
= .
of methane
13. ④
k3④ It Fs also possible to calculate enthalpy of reaction using
bond enthalpy .
Do HEEbond enthalpy
otreaastnts-Zbondenthpafopgqot.LI
:
-
calculate the enthalpy change CAH) of the following reaction .
GHzCg) t
Iz 021g) - 2 Coz Cg) t HD Cg)
Given bond enthalpies of various bonds:-
Dc-
H
HE 414 KS mot
'
Bec HE 814 KJmot
'
Do H-0=499 KT molt
A ⇐o
H-0=724 KJ mot
'
SH:-
Caegtiation tf
, elaborate af, D
Ao- HH-0=640 KImom
(H -
CE C -
H
)t
Z (0=0) → 2 (o =
⇐o
) t CH-
o-
H
)
As we know,
DrHo -
-
fsumotboenadeeannthglpiesf-
(sum of bond enthalpies
of of products ]
=
Hbc-
HH't BecHo -
IIDo H-9-
14 D⇐otto -12 Do-
H Hof
=
(2x 414 t 810T
Ex 499) -
(4×724+2×460) KT
=
(2885.5-3816) KJ
= -
930.5 KJ
←
# Enthalpy of solution , Dsoe Ho or
↳The enthalpy change when one mole of solute is dissolved completely in
specific amount of solvent or water is called enthalpy of solution.
°
It solvent Ps in excess i.e. the interactions between the ions too solute
molecules ) are
negligible then the enthalpy change is called enthalpy of solution
at infinite dilution.
°
Aoe H =
Dealtice Hot Dhyd Ho
14. ⑤
# Enthalpy of Hydration ,
Dmd Ho : when one mole of anhydrous or partially
hydrated salt combines with required number of moles of water to form a
specific hydrate .
egfr (u soy G) t 5Hall) → CUSOy .
5h20 Is)
# Enthalpy of NeutralBatton ( Dn Ho) :
-
The enthalpy change accompanying the
formation of one mole of H2O by combination of one Mol Ht ions furnished by
acid and one mole of
-
OH Tons furnished by base in dilute solutions at the
standard conditions .
• Anti offstrong acid -
strong base) -
57 .
I .
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will be uploaded in L-2 days on
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