chapter 4 final Thermo.pdf - Chapter 4 The first Law of...

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Chapter 4: The first Law of Thermodynamics: Control Volumes The first law is discussed for closed systems in Chapter 3. In this Chapter, we extend the conservation of energy to systems that involve mass flow across their boundaries, control volumes . Any arbitrary region in space can be selected as control volume . There are no concrete rules for the selection of control volumes. The boundary of control volume is called a control surface . Conservation of Mass Like energy, mass is a conserved property, and it cannot be created or destroyed. Mass and energy can be converted to each other according to Einstein’s formula: E = mc 2 , where c is the speed of light. However, except for nuclear reactions, the conservation of mass principle holds for all processes. For a control volume undergoing a process, the conservation of mass can be stated as: Fig. 4-1: Conservation of mass principle for a CV. The conservation of mass can also be expressed in the rate form: The amount of mass flowing through a cross section per unit time is called the mass flow rate and is denoted by . The mass flow rate through a differential area dA is: dm°= ρV n dA
where V is the velocity component normal to dA. Thus, the mass flow rate for the entire cross-section is obtained by: ) kg/s ( dA V m A n = ρ Assuming one-dimensional flow, a uniform (averaged or bulk) velocity can be defined: m°= ρ V A (kg/s) where V (m/s) is the fluid velocity normal to the cross sectional area. The volume of the fluid flowing through a cross-section per unit time is called the volumetric flow, V°: /s) (m 3 VA dA V V A n = = The mass and volume flow rate are related by: m°= ρ V°= V°/ v. Conservation of Energy For control volumes, an additional mechanism can change the energy of a system: mass flow in and out of the control volume. Therefore, the conservation of energy for a control volume undergoing a process can be expressed as total energy crossing boundary as heat and work + total energy of mass entering CV total energy of mass leaving CV = net change in energy of CV CV mass out mass in E E E W Q = + + , , This equation is applicable to any control volume undergoing any process. This equation can also be expressed in rate form: dt dE dt dE dt dE W Q CV mass out mass in / / / , , = + + Fig. 4-2: Energy content of CV can be changed by mass flow in/out and heat and work interactions. Mass in Mass out Q W Control volume
Work flow: is the energy that required to push fluid into or out of a control volume. Consider an imaginary piston (that push the fluid to CV) where the fluid pressure is P and the cross sectional area is A. The force acting on the piston is F = PA. Fig. 4-3: schematic for flow work. The work done in pushing the fluid is: W flow = F.s = PA.s = PV (kJ) or in a unit basis, w flow = W flow / m = Pv (kJ/kg) Note that the flow work is expressed in terms of properties.

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