Thermodynamics

250 | Thermodynamicssince the initial state of the system is simply the line conditions of thesteam. This result is identical to the one obtained with the uniform-flowanalysis. Once again, the temperature rise is caused by the so-called flowenergy or flow work, which is the energy required to move the fluid duringflow.EXAMPLE 5–13Cooking with a Pressure CookerSystemboundary˙H 2 Om 1 = 1 kgV = 6 LP = 75 kPa (gage)VaporQ in = 500 WLiquidFIGURE 5–49Schematic for Example 5–13.P = 175 kPaT = T sat@P = 116°CFIGURE 5–50As long as there is liquid in a pressurecooker, the saturation conditions existand the temperature remains constantat the saturation temperature.A pressure cooker is a pot that cooks food much faster than ordinary pots bymaintaining a higher pressure and temperature during cooking. The pressureinside the pot is controlled by a pressure regulator (the petcock) that keepsthe pressure at a constant level by periodically allowing some steam toescape, thus preventing any excess pressure buildup.Pressure cookers, in general, maintain a gage pressure of 2 atm (or 3 atmabsolute) inside. Therefore, pressure cookers cook at a temperature of about133°C (or 271°F) instead of 100°C (or 212°F), cutting the cooking time byas much as 70 percent while minimizing the loss of nutrients. The newerpressure cookers use a spring valve with several pressure settings rather thana weight on the cover.A certain pressure cooker has a volume of 6 L and an operating pressureof 75 kPa gage. Initially, it contains 1 kg of water. Heat is supplied to thepressure cooker at a rate of 500 W for 30 min after the operating pressure isreached. Assuming an atmospheric pressure of 100 kPa, determine (a) thetemperature at which cooking takes place and (b) the amount of water left inthe pressure cooker at the end of the process.Solution Heat is transferred to a pressure cooker at a specified rate for aspecified time period. The cooking temperature and the water remaining inthe cooker are to be determined.Assumptions 1 This process can be analyzed as a uniform-flow process sincethe properties of the steam leaving the control volume remain constant duringthe entire cooking process. 2 The kinetic and potential energies of the streamsare negligible, ke pe 0. 3 The pressure cooker is stationary and thus itskinetic and potential energy changes are zero; that is, KE PE 0 andE system U system . 4 The pressure (and thus temperature) in the pressurecooker remains constant. 5 Steam leaves as a saturated vapor at the cookerpressure. 6 There are no boundary, electrical, or shaft work interactionsinvolved. 7 Heat is transferred to the cooker at a constant rate.Analysis We take the pressure cooker as the system (Fig. 5–49). This is acontrol volume since mass crosses the system boundary during the process.We observe that this is an unsteady-flow process since changes occur withinthe control volume. Also, there is one exit and no inlets for mass flow.(a) The absolute pressure within the cooker isP abs P gage P atm 75 100 175 kPaSince saturation conditions exist in the cooker at all times (Fig. 5–50), thecooking temperature must be the saturation temperature corresponding tothis pressure. From Table A–5, it isT T sat @ 175 kPa 116.04°Cwhich is about 16°C higher than the ordinary cooking temperature.