Thermodynamics

Chapter 5 | 243at 25°C. Neglecting any pressure drops, determine (a) the mass flow rate ofthe cooling water required and (b) the heat transfer rate from the refrigerant towater.Solution Refrigerant-134a is cooled by water in a condenser. The mass flowrate of the cooling water and the rate of heat transfer from the refrigerant tothe water are to be determined.Assumptions 1 This is a steady-flow process since there is no change withtime at any point and thus m CV 0 and E CV 0. 2 The kinetic andpotential energies are negligible, ke pe 0. 3 Heat losses from the systemare negligible and thus Q . 0. 4 There is no work interaction.Analysis We take the entire heat exchanger as the system (Fig. 5–37). Thisis a control volume since mass crosses the system boundary during theprocess. In general, there are several possibilities for selecting the controlvolume for multiple-stream steady-flow devices, and the proper choicedepends on the situation at hand. We observe that there are two fluidstreams (and thus two inlets and two exits) but no mixing.(a) Under the stated assumptions and observations, the mass and energybalances for this steady-flow system can be expressed in the rate form asfollows:Mass balance:m # in m # outfor each fluid stream since there is no mixing. Thus,Energy balance:E # in E # out dE system >dt 0⎫⎪⎪⎪⎬⎪⎪⎪⎭⎫⎪⎪⎬⎪⎪⎭Rate of net energy transferby heat, work, and massm # 1 m # 2 m # wm # 3 m # 4 m # RRate of change in internal, kinetic,potential, etc., energiesE # in E # outm # 1h 1 m # 3h 3 m # #2h 2 m 4 h 4 1since Q # 0, W # 0, ke pe 02Combining the mass and energy balances and rearranging givem # w(h 1 h 2 ) m # R(h 4 h 3 )Now we need to determine the enthalpies at all four states. Water exists as acompressed liquid at both the inlet and the exit since the temperatures atboth locations are below the saturation temperature of water at 300 kPa(133.52°C). Approximating the compressed liquid as a saturated liquid atthe given temperatures, we haveh 1 h f @ 15° C 62.982 kJ/kgh 2 h f @ 25° C 104.83 kJ/kgThe refrigerant enters the condenser as a superheated vapor and leaves as acompressed liquid at 35°C. From refrigerant-134a tables,P 3 1 MPaT 3 70C f h 3 303.85 kJ/kg (Table A–13)¡ 0 (steady)(Table A–4)P 4 1 MPaT 4 35C f h 4 h f @ 35C 100.87 kJ/kg (Table A–11)R-134a370°C1MPa225°CFIGURE 5–37Water15°C300 kPa1Schematic for Example 5–10.435°C