Thermodynamics

248 | Thermodynamicsone of these with satisfactory results. The degree of satisfaction depends onthe desired accuracy and the degree of validity of the assumptions made.EXAMPLE 5–12Charging of a Rigid Tank by SteamA rigid, insulated tank that is initially evacuated is connected through avalve to a supply line that carries steam at 1 MPa and 300°C. Now the valveis opened, and steam is allowed to flow slowly into the tank until the pressurereaches 1 MPa, at which point the valve is closed. Determine the finaltemperature of the steam in the tank.Solution A valve connecting an initially evacuated tank to a steam line isopened, and steam flows in until the pressure inside rises to the line level.The final temperature in the tank is to be determined.Assumptions 1 This process can be analyzed as a uniform-flow process sincethe properties of the steam entering the control volume remain constant duringthe entire process. 2 The kinetic and potential energies of the streams arenegligible, ke pe 0. 3 The tank is stationary and thus its kinetic andpotential energy changes are zero; that is, KE PE 0 and E system U system . 4 There are no boundary, electrical, or shaft work interactionsinvolved. 5 The tank is well insulated and thus there is no heat transfer.Analysis We take the tank as the system (Fig. 5–47). This is a control volumesince mass crosses the system boundary during the process. We observe thatthis is an unsteady-flow process since changes occur within the control volume.The control volume is initially evacuated and thus m 1 0 and m 1 u 1 0.Also, there is one inlet and no exits for mass flow.Noting that microscopic energies of flowing and nonflowing fluids are representedby enthalpy h and internal energy u, respectively, the mass andenergy balances for this uniform-flow system can be expressed asImaginarypistonP i = 1 MPaT i = 300°CSteamP i = 1 MPa (constant)m i = m 2m 1 = 0P 2 = 1 MPaT 2 = ?P 2 = 1 MPa(a) Flow of steam intoan evacuated tank(b) The closed-systemequivalenceFIGURE 5–47Schematic for Example 5–12.