Thermodynamics

⎫⎪⎬⎪⎭⎫⎪⎬⎪⎭Mass balance:Energy balance:0m in m out ¢m system Sm i m 2 m 1 m 2Chapter 5 | 249E in E out ¢E system⎫⎪⎬⎪⎭⎫⎪⎬⎪⎭Net energy transferChange in internal, kinetic,by heat, work, and masspotential, etc., energiesm i h i m 2 u 2 (since W Q 0, ke pe 0, m 1 0)Combining the mass and energy balances givesu 2 h iThat is, the final internal energy of the steam in the tank is equal to theenthalpy of the steam entering the tank. The enthalpy of the steam at theinlet state isP i 1 MPaT i 300C f h i 3051.6 kJ/kg (Table A–6)which is equal to u 2 . Since we now know two properties at the final state, it isfixed and the temperature at this state is determined from the same table to beDiscussion Note that the temperature of the steam in the tank has increasedby 156.1°C. This result may be surprising at first, and you may be wonderingwhere the energy to raise the temperature of the steam came from. Theanswer lies in the enthalpy term h u Pv. Part of the energy representedby enthalpy is the flow energy Pv, and this flow energy is converted to sensibleinternal energy once the flow ceases to exist in the control volume, and itshows up as an increase in temperature (Fig. 5–48).Alternative solution This problem can also be solved by considering theregion within the tank and the mass that is destined to enter the tank as aclosed system, as shown in Fig. 5–47b. Since no mass crosses the boundaries,viewing this as a closed system is appropriate.During the process, the steam upstream (the imaginary piston) will pushthe enclosed steam in the supply line into the tank at a constant pressure of1 MPa. Then the boundary work done during this process is2W b,in P i dV P i 1V 2 V 1 2 P i 3V tank 1V tank V i 24 P i V i1P 2 1 MPau 2 3051.6 kJ/kg fT 2 456.1°Cwhere V i is the volume occupied by the steam before it enters the tank andP i is the pressure at the moving boundary (the imaginary piston face). Theenergy balance for the closed system givesSteamT i = 300°CT 2 = 456.1°CFIGURE 5–48The temperature of steam rises from300 to 456.1°C as it enters a tank as aresult of flow energy being convertedto internal energy.E in E out ¢E systemNet energy transferChange in internal, kinetic,by heat, work, and masspotential, etc., energiesW b,in ¢Um i P i v i m 2 u 2 m i u iu 2 u i P i v i h i