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Unformatted text preview: MECH 310 Thermodynamics I November 20, 2007 American University of Beirut, Fall 2007 Handout # 1 First Law of Thermodynamics 1 Subject of Study Any scientific analysis is incomplete without precise specification of the subject of study. When applying the laws of thermodynamics, specification of the subject of study is usually the first thing to do. When the subject of study is matter of fixed identity, i.e. it always consists of the same molecules, then we are referring to a control mass . Examples include a block of copper, the gas inside a sealed container, etc. Tracking the same molecules is not always an easy task and is at times impossible. Consider, for example combustion of fuel and air in the combustion chamber of a gas turbine. Upon combustion, the identity of molecules change. Not only that, molecules which are at time t inside the combustion chamber moved to somewhere else, say the turbine, at t + Δ t . So if we are interested in what happens inside the combustor, we find ourselves chasing molecules far from the combustor at later times. So it makes sense in this case, to take the combustor itself (or the volume enclosed by the combustor walls) as the subject of study, with (fuel + air) molecules flowing in across the boundary and products molecules flowing out across the combustor boundary. This is an example of a control volume ; a predefined volume that usually contains a region of interest or a device of interest. The boundary of the control volume across which material flows is called the control surface . 2 Conservation Laws in Thermal and Fluid Sciences 1. conservation of mass (continuity) 2. conservation of momentum (Newton’s second law) 3. conservation of energy (first law of thermodynamics) 4. non-conservation of exergy (second law of thermodynamics) The field of thermal and fluid sciences consists usually of the following interconnected areas: thermodynamics (MECH 310, laws 1, 3 and 4), fluid mechanics (MECH 410, laws 1 and 2), and heat transfer (MECH, laws 1 and 3). 3 Conservation of Mass 3.1 Conservation of Mass for a Control Mass Since a control mass (C.M.) consists of matter of fixed identity, then by definition the mass of a control mass is conserved, i.e. dm C.M. dt = 0 ⇒ d dt Z V ρd V = 0 (1) 1 at time t x z y x ( t ) x ( t ) + d x ( t ) u d x ( t ) = u dt at time t + dt Figure 1: Material derivative is change of property as the particle is moving. where ρ is the density (kg/m 3 ) is generally a function of time and space. The volume of the control mass is V and in cartesian coordinates d V = dxdy dz . In equation (1), one should not mistake d () /dt for ∂ () /∂t ; the latter is the derivative in time holding every- thing else fixed, i.e. at a constant position....
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