Introduction 1-5 Methods of analysis The system that you are attempting to analyze Basic mechanics: free-body diagram thermod ynamics: closed system(terms: system and control volume)
Introduction • 1-5 Methods of analysis • The system that you are attempting to analyze Basic mechanics : free-body diagram thermodynamics: closed system(terms: system and control volume)
1-5. 1 System and Control Volume a system is defined as a fixed identifiable quantity of mass; the system boundaries separate the system from the surroundings(fixed or movable), no mass crosses the system boundaries A control volume is an arbitrary volume in space through which fluid flows. The geometric boundary of the comtrol volume is called the control surface (include real or imaginary)
1-5.1 System and Control Volume • A system is defined as a fixed, identifiable quantity of mass; the system boundaries separate the system from the surroundings(fixed or movable), no mass crosses the system boundaries. • A control volume is an arbitrary volume in space through which fluid flows. The geometric boundary of the comtrol volume is called the control surface.(include real or imaginary)
1-5.2 Differential versus Integral Approach The basic laws can be formulated in terms of infinitesimal or finite systems and control volumes The first case the resulting equation are differential equation The integral formulations of basic laws are easier to treat analytically, for deriving the control volume equation, we need the basic laws of mechanics and thermodynamics, formulated in terms of finite systems
1-5.2 Differential versus Integral Approach • The basic laws can be formulated in terms of infinitesimal or finite systems and control volumes. • The first case the resulting equation are differential equation. • The integral formulations of basic laws are easier to treat analytically, for deriving the control volume equation , we need the basic laws of mechanics and thermodynamics ,formulated in terms of finite systems
1-5.3 Methods of Description Use of the basic equations applied to a fixed, identifiable quantity of mass, keep track of identifiable elements of mass(in particle mechanics the lagrangian method of description) Example: th eapplication of Newton's second law to a particle of fixed mass Consider a fluid to be composed of a very large number of particle whose motion must be described With control volume analyses, the Eulerian on the properties of a flow at a given point in space as a function of time
1-5.3 Methods of Description • Use of the basic equations applied to a fixed , identifiable quantity of mass, keep track of identifiable elements of mass(in particle mechanics: the Lagrangian method of description) • Example: th eapplication of Newton’s second law to a particle of fixed mass • Consider a fluid to be composed of a very large number of particle whose motion must be described • With control volume analyses, the Eulerian on the properties of a flow at a given point in space as a function of time
EXAMPLE PROBLEM 1.1 GIVEN: Piston-cylinder containing O2, m-0.95Y 71=27CT2=627C p= constant= 150 kPa(abs FIND: Q SOLUTION We are dealing with a system, m=0.95 kg Basic equation: First law for the system, Q12-Wn2- E2-Er Assumptions: (1) E= U, since the system is stationary (2) Ideal gas with constant specific heats Under the above assumptions, E2-E1=U2-U1=m(-)=mcn(T2-1 The work done during the process is moving boundary work P v=p(H2-V1) For an ideal gas, Pt a mRT. Hence Wn= mR(T2-T1). Then from the first law equation, On= E2-E+Wn T1)+mR(2-T) Q12=m(T2-71)c+R Q12=mcp(72-71){R=cp-c From the Appendix, Table A 6, for O2, Cp =909. 4 J/(kg. K). Solving for @n2, we obtain 095kg909Jx60K =518kJ K The purpose of this problem was to review the use of () the first law of thermodynamics for a system, and (i) the equation of state for an ideal gas