HOMEWORK 4 (Due on Oct. 1 at beginning of class) Where you require data on the thermodynamic properties of water, refer to Fig. B3 in Appendix B of the book. 1. A quantity of water, initially saturated liquid, is heated in a quasistatic constant pressure process until it is in the saturated vapor state. The mass is 20 Kg and the pressure is 0.5 MPa. (a) What is the initial temperature? Does the temperature vary during this process? (b) Obtain the initial and flnal volumes. Determine the volume when 50% of the uid is in the vapor phase. (c) Calculate the external work performed on the uid during the process. (d) Determine the change in the internal energy of the system in this heating process. (e) What is the heat input? (f) Instead of the heating process described, the volume is suddenly increased from its initial to flnal value in a free expansion process (that is, the process is adiabatic and no work is done). What is the flnal temperature? Determine the mass of water remaining in the liquid phase. (g) At the conclusion of the free expansion process described in (f), the system is heated at constant volume until the saturated vapor phase is reached. Determine the heat input to the system in this process and the work done. 2. An evacuated vessel, of volume 40 m3, is connected through a closed valve to a second vessel, of volume 0.004 m3, which is fllled with saturated liquid water at a pressure of 20 MPa. The valve is opened and the system reaches equilibrium, the temperature being then the same in both vessels. The process is adiabatic. (a) What is the equilibrium temperature? (b) The composite system is cooled until the temperature is 10 oC. Determine the heat input to the system. 3. (a) A uid in steady ow passes through a simple adiabatic nozzle, as shown in Fig. 5.13 of the book. Given that the velocity of the uid at cross-section a is ca, show that the velocity of the uid at cross-section b, cb, is given by: cb = q c2a +2(ha ¡hb) where h is the speciflc enthalpy, H=m, with m the mass. (b) If, in addition, the uid is incompressible show that: cb = q c2a +2v(Pa ¡Pb) (1) 1 where v is the speciflc volume, V=m, and P is the pressure. Equation (1) can be re-written as: 1 2?c 2 b +Pb = 1 2?c 2 a +Pa where ? = 1=v is the density. As a result, along a uid ow line: 1 2?c 2 +P = cte This expression re ects the so-called Venturi efiect for ideal (non-viscous) liquid ow: If the speed of the liquid increases, its pressure must decrease. This is exploited in many applications. For example, it is used to achieve moderate vacuums in containers: Consider water owing through a pipe with a narrowing. The speed at the narrowing increases and a result the pressure decreases. If the container is connected to the narrowing, the lower pressure in the narrowing of the pipe will suck gas from the container. The higher the speed of the liquid, the larger the vacuum. 2
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