Lecture Notes on Thermodynamics 2008

Lecture Notes on Thermodynamics 2008 Chapter 10 Thermodynamics Relations Prof. Man Y. Kim, Autumn 2008, ⓒmanykim@chonbuk.ac.kr, Aerospace Engineering, Chonbuk National University, Korea

Two Important Partial Derivative Relations Consider a variable z which is a continuous function of x and y : and (*) If we take y and z as independent variables : and (**) Substitute eq.(**) into (*) : Since there are only 2 independent variables, Reciprocity relation Cyclic relation

Maxwell Relations Maxwell Relations : Four equations relating the properties P, v, T, and s for a simple compressible system of fixed chemical composition 2 Gibbs equations in Chapter 6 : Helmholtz free energy : Gibb’s free energy : Since u, h, a, and g are total derivative ;

Clapeyron Equation Clapeyron Equation : P, v, T를 통해 증발엔탈피( )와 같은 상변화와 관계있는 엔탈피 변화를 구하는 관계식 Let’s consider the 3rd Maxwell relation ; 상변화가 일어나는 동안 압력은 온도에만 의존하고 비체적에는 무관한 포화압력을 유지함. 즉, 등온 액체-증기 상변화과정에 대해서 세번째 Maxwell 관계식을 적분하면 ; 이 과정 동안 압력도 일정하게 유지되므로, 따라서,

Clapeyron-Clausius Equation Clapeyron-Clausius Equation : Clapeyron 방정식에 약간의 근사를 사용하여 액체-증기와 고체-증기의 상변화에 적용함. 저압상태일 때 ; 증기를 이상기체로 가정하면 ; 따라서, 작은온도구간에 대하여 는 어떤 평균값으로 일정하므로, 윗 식에서 를 (승화엔탈피)로 대치함으로서 고체-증기 영역에서도 사용함.

Relations between du, dh, ds, Cv and Cp(1/6) • Change of Internal Energy If, If, since Therefore, Finally, and

Relations between du, dh, ds, Cv and Cp(2/6) • Change of Internal Energy - Example

Relations between du, dh, ds, Cv and Cp(3/6) • Change of enthalpy If, If, since Therefore, Finally, and

Relations between du, dh, ds, Cv and Cp(4/6) • Change of Entropy If, Therefore, If, Therefore,

Relations between du, dh, ds, Cv and Cp(5/6) • Specific Heat (1/2) Substitute (3’) into (3) ;

Relations between du, dh, ds, Cv and Cp(6/6) • Specific Heat (2/2) We know the cyclic relations as : where, : volume expansivity : isothermal compressibility Comments :

Joule-Thomson Coefficient (1/2) • Joule-Thomson Coefficient : 교축(h=constant) 과정 중의 유체의 온도 변화

Joule-Thomson Coefficient (2/2)

No Homework ! http://procom.chonbuk.ac.kr 14 Propulsion and Combustion Lab.

Lecture Notes on Thermodynamics 2008