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- Check your Understanding Show that QhQh=QcQc for the hypothetical engine of Figure 4.10 The second property to be demonstrated is that all reversible engines operating between the same two reservoirs have the same efficiency. To this, stat with the two engines D and E of Figure 4.10 (a), which are operating between two common heat reservoirs at temperatures Th and Tc . First, assume that D is a reversible engine and that E is a hypothetical irreversible engine that has a higher efficiency than D. If both engines perform the same amount of work W per cycle, it follows from Equation 4.2 that QhQh . It then follows from the first law that QcQc . Figure 4.10 (a) Two uncoupled engines D and E working between the same reservoirs. (b) The engines, With D working reverse. Suppose the cycle of D is so that it operates as a refrigerator, and the two engines are coupled such that the work output of E is used to drive D, as shown in Figure 4.10(b). Since QhQh and QcQc , the net result of each cycle is equivalent to a spontaneous transfer of heat from the cold reservoir to the hot reservoir, a process second law does not allow. The original assumption must therefore be wrong, and it is impossible to construct an irreversible engine such that E is more efficient than the reversible engine D. Now it is quite easy to demonstrate that the efficiencies of all reversible engines operating between the same reservoirs are equal. Suppose that D and E are reversible engines. If they are as shown in Figure 4.10(b), the efficiency of E cannot be greater than the efficiency of D, or second law would violated. If both engines are then reversed, the same reasoning implies that the efficiency of D cannot be greater than the efficiency of E. Combining these results leads to the conclusion that all reversible engines working between same two reservoirs have the same efficiency.Calculate the internal energy of 15 mg of helium at a temperature of 0 . `What does it mean to say that two systems are in thermal equilibrium?
- A mole of ideal monatomic gas at 0 and 1.00 atm is warmed up to expand isobarically to triple its volume. How much heat is transferred during the process?An infrared heater for a sauna has a surface area of 0.050 m2 and an emissivity of 0.84. What temperature must it run at if the required power is 360 W? Neglect the temperature of the environment.Explain how the maximum possible heat transferrate Q.max in a heat exchanger can be determined when themass flow rates, specific heats, and the inlet temperatures ofthe two fluids are specified. Does the value of Q.max dependon the type of the heat exchanger?
- One ton of liquid water at 80C is brought into awell-insulated and well-sealed 4-m * 5-m * 7-m room initiallyat 22C and 100 kPa. Assuming constant specific heatsfor both air and water at room temperature, determine (a) thefinal equilibrium temperature in the room and (b) the totalentropy change during this process, in kJ/K.How much thermal energy must be added to 3.00 moles of monatomic ideal gas tat 300 K kept at constant volume of 1.5 L in order to raise the temperature to 400 K ? How would the result change if the ideal gas in the example is diatomicAn inventor claims to have invented an adiabaticsteady-flow device with a single inlet–outlet that produces230 kW when expanding 1 kg/s of air from 1200 kPa and300C to 100 kPa. Is this claim valid?
- A counter-flow double-pipe heat exchanger is to heat water from 20°C to80°C at a rate of 1.2 kg/s. The heating is to be accomplishedby geothermal water available at 160°C at a mass flow rate of 2 kg/s. Theinner tube is thin-walled and has a diameter of 1.5 cm. The overall heat transfercoefficient of the heat exchanger is 640 W/m2?K. Using the effectiveness–NTUmethod, determine the length of the heat exchanger required to achieve thedesired heating.An aluminum capwhich serves as acover to a glasspyrex jar is tightlyattached to the glass;To open the jar, itwas exposed to ahot water bath andthe temperaturewas noted at 70Celsius. The insidediameter of the capis 6.0 cm at 30Celsius. Find thedifference in radius(cm) that will resultby this methodCold water enters a counter-flow heat exchanger at 10°C at a rate of 8 kg/s, where it is heated by a hot-water stream that enters the heat exchanger at 70°C at a rate of 2 kg/s. Assuming the specific heat of water to remain constant at cp = 4.18 kJ/kg?K, determine the maximum heat transfer rate and the outlet temperatures of the cold- and the hot-water streams for this limiting case.