1 st thermodynamics law & its application

1stthermodynamics law & its application (The First Law of Thermodynamics) U = Q -W

Content 1.1Introduction to thermodynamics 1.21st thermodynamics law 1.3Quasi-static & reversible process 1.4Enthalpy 1.5Heat capacity 1.6Application 1.7 Real gases 1.8Thermal chemistry 1.9Hess’s law 1.10Several thermal effects 1.11 Kirchoff law

1.1 Introduction to thermodynamics • Research the interactive transformation among the heat, work and other form energy. • Research the energy effect which takes place in the different physical and chemical changes; • Research the direction and limitation of chemical changes. • The mechanics, rate and microcosmic properties are unknown, so we only think the possibility but the reality.

1.1.1 System and surroundings System We call the fixed research object as system, also substance system. System is separated from the other parts, the boundary can be visual or imaginable. Surroundings The part which has reciprocity with system, or correlate with the system closely.

1.1.1.1 Open system Both matter and energy exchange take place between system and surroundings.

1.1.1.2 Closed system It has no matter exchange, but energy exchange between system and surroundings.

1.1.1.3 Isolated system • Neither matter nor energy exchange takes place between system and surroundings. • Sometimes both the closed system and its surroundings are thought as an isolated system.

1.1.2 System properties The macrocosmic measurable properties are used to describe thermodynamics state of the system, so all these properties are called thermodynamics variables. 1.1.2.1 Extensive properties(capacity properties) Numerical value is directly ratio with system quantity, volume (V), entropy (S). These properties can be summed up.

1.1.2.2 Intensive properties • Its numerical value depends on its own character of the system, it has nothing to do with the quantity of system. T, P. • The capacity properties of every mole material quantity are designated as intensive properties, such as molar heat capacity.

1.1.3 Thermodynamic equilibrium • Thermal equilibrium • Mechanical equilibrium • Phase equilibrium • Chemical equilibrium

1.1.4 State function Some values ofsystem properties have nothing to do with the history of the system, they are decided by system state.The change values depend on the initial and the final state, and have nothing to do with the change ways. This kind of physical quantity is called state function.

1.1.4.2 State function characters • Different ways come to the same final, the value change is the same ; • 异途同归，值变相等； • Move one cycle, numerical value go back to the origin. • 周而复始，数值还原。 • In mathematics, State function has the character of full differential.

1.1.5 Heat and work 1.1.5.1 Heat The energy transfers from system to surrounding because of the different temperature. Q stands for heat. System absorbs heat, Q>0; System gives out heat, Q<0.

1.1.5.2 Work • Except for heat, any other energy transformation forms from system to surrounding. • W stands for work. • System export work to surrounding, W>0; • Surrounding export work to system, W<0. • Both Q and W are not state function, their numerical value is related with the change ways

1.2 The first law of thermodynamics 1.2.1 Heat equivalent of work • From 1840, Joule and Mayer had confirmed the relationship of heat and work by many different experiment: 1 cal=4.1840 J • Energy conversation law: In the nature, every substance has energy, which has different change forms. It can change from one form to another, but during the change, the total energy is unchangeable.

1.2.2 Thermodynamics energy • Thermodynamic energy (internal energy): the summation of system internal energy. It includes the translation energy of the molecule motion, and molecule internal energy. • Thermodynamics energy is state function, U stands for it, its absolute value is unknown. We can only work out its change value.

1.2.3 The first law of thermodynamics U = Q -W dU =Q -W • Energy conservation and translation law have special forms in the area of heat phenomena, it shows that thermodynamic energy, heat and work can change each other. • The 1st kind of the perpetual machine can not be made-up. • ( It does not need environment to provide energy, but can export work perpetually.)

1.3 quasi-static process & reversible process Work and process quasi-static process Reversible process

1.3.1 Work and process The system volume expands from V1 to V2. through 4 different ways. T = constant; outside pressure pe; work material: the fixed ideal gas. 1.3.1.1 Free expansion 1.3.1.2 The same temperature expansion

1.3.1.3 Expansion many times at the same pressure • The system volume expand from V1 to V’ by conquering the outside pressure P’ ; • The system volume expand from V’ to V” by conquering the outside pressure P” ; • The system volume expand from V” to V2 by conquering the outside pressure P2 .

1.3.1.3 Page 2 • The work of the system equals to the summation work of the three process. • The more the times of expansion,The less difference between system and outside pressure, the more it works.

1.3.1.4 Outside press is infinite smaller than inside press Work: This process can approximately be regarded as a reversible process, the work is the most.

1.3.1.5 Compress process Compress the volume from V1 to V2, It has three ways as following: 1.3.1.5.1 Compress at constant pressure Outside pressure: P1, The volume decrease from V2 to V1,

1.3.1.5.2 Compress many times at the same pressure • Volume from V2 to V” by the pressure P” ; • Volume from V” to V’ by the pressure P’ ; • Volume from V’ to V1 by the pressure P1 .

1.3.1.5.3 Reversible compression Both system and surrounding can get back to the original state.

1.3.1.6 Brief summary

1.3.2 Quasi-static process • Every moment in the process, system approaches to the equilibrium state, so that, within the every little time dt, the state parameters of every system part have certain value, the whole process is considered to be composed by a serious of states which approach equilibrium states. • Quasi-static process is an ideal process.

1.3.3 Reversible process System changes from state (1) to (2) after some processes, if both the system and surrounding can go back to the origin state without leaving any perpetual changes. It is called as Reversible process.Otherwise, Irreversible process.

1.3.3 Reversible process If the quasi-static expansion process don’t dissipate any energy, it can be regarded as a reversible process. During the process, every step approach to the equilibrium state, it can process adversely, from the initial state to the final, and then returns from the final state to the initial state,both the system and surround-ing can get back to the original state.

1.3.3.2 Characters of reversible process (1) During the state changing, the difference of the impetus and the resistance is infinitesimal,system and surrounding are always approaching to the equilibrium state infinitely; (2) After the system changing in a cycle, both the system and surrounding go back to the initial state, there is no dissipation during the changing. (3) During the isothermal reversible process, system export the biggest work to surrounding, while surrounding export the lowest work to system.

1.3.4 Some process 1.3.4.1 Isothermal process During the change, the final temperature of the system is the same with the initial, and it equals to the surrounding temperature. 1.3.4.2 Isobaric process During the change, the final pressure of the system is the same with the initial, and it equals to the surrounding pressure.

1.3.4.3 Isochoric process During the process, the system volume keeps unchangeable. 1.3.4.4 Adiabatic process During the change, no heat transfer happens between system and surrounding. 1.3.4.5 Cyclic process The process of the system goes back to the initial state after a series of changes.

1.4 Enthalpy In order to use conveniently, new state function is defined as follows: = △H under the same pressure, the system does not do other work, the change of enthalpy equals to the isobaric thermal effect Qp.

or 1.5 Heat capacity Specific heat capacity: The heat capacity of the substance which quality is 1g (or 1 Kg). Its unit is 1.5.1 Average heat capacity

1.5.2 Isobaric & isometric Heat capacity Isobaric Cp: Isometric Cv:

1.6 Application Gay-Lussac-Joule experiment Ideal gas U and H Ideal gas Cp-Cv Adiabatic process

1.6.1 Gay-Lussac-Joule experiment In 1807, Gay-Lussac-Joule did the experiment separately as following : Put two containers of the same capacity in the water- bath, fill the left ball with gas, the right ball is vacuum, the gas rush to the right one through the left one, and then it gets equilibrium.

1.6.1.2 Gay-Lussac-Joule experiment The temperature in the water-bath does not change, that is , Q=0, because the volume of the system is composed both of the balls, it does not export work in the system, W=0: according to the first law of thermodynamics,we can get ∆ U=0.

1.6.2 Ideal gas U and H From the Gay-Lussac-Joule experiment, we can conclude that internal energy and enthalpy are temperature function. Cv=f (T), Cp =f (T)

1.6.3 Ideal gas Cp-Cv • In the isometric process, when the temperature ascends, all of the heat absorbed by the system is used to increase the thermodynamics energy. • But in the isobaric process, beside increasing U, the system needs to absorb more heat to do expansion work externally. • So, Cv<Cp

1.6.4 Adiabatic process 1.6.4.1 Work of adiabatic process dU =Q -W =-W • If the system exports work, the thermal energy decreases. • If the system get work, internal energy increases.

1.6.4.2 Equation of adiabatic process K1 K2 K3 are constants

1.6.4.3 Calculation of adiabatic process (1) The work of the adiabatic reversible process of ideal gas

1.6.4.4 Calculation of adiabatic process (2) Work of adiabatic process W =- U Cv(T1-T2 ) because we do not introduce any other limitation conditions, this formula can beapplied in adiabatic process of closed system which has fixed composing, need not always ideal gas, or reversible process.

1.7 Real gas 1.7.1 Joule-Thomsoneffect Joule and Thomson designed a new experiment in 1852, which was called throttling process.

i.e. Analysis • In Adiabatic contain, Q=0 • In the left, surrounding does Compress work. • In the right, system does expand work

1.7.2 Enthalpy of realgases • H2=H1 • H=constant • But, U=f (T,V)

1.7.3 van der Waals equation a/ V2m in the formula is the emendation item of pressure, internal pressure: b is the emendation item of volume occupied by gas molecule.

1.8 Thermochemistry Reaction effect: After the reaction happens in the system, we make the product temperature back tothe initial state of the reaction, system discharges or absorbs energy. Isobaric thermal effect: Qp= ∆ H Isometric thermal effect: Qv= ∆ U

Reactant Product （3） (2)isometric resultant 1.8.1 Isobaric & isometric thermal effect

1 st thermodynamics law & its application