4.An inventor claims to have developed a device that executes a power cycle while operating between reservoirs at 500 and 300 K that has a thermal efficiency of 40% . Is it possible? Why? (15%)

(3) Fourier，s law of conduction

(4) Newton5s law of cooling

(5) the principles of increase of entropy

3 .Try to use temperature-entropy diagram to explain the ideal Rankine cycle. What are effects of boiler and condenser pressures on thermal efficiency of the Rankine cycle.' (15%)

5.A small nuclear reactor is cooled by passing liquid sodium (Na) through it. The liquid sodium leaves the reactor at 0.2 MPa and 400°C. It is cooled to 320°C by passing through a heat exchanger before returning to the reactor. In the heat exchanger, heat is transferred from the liquid sodium to water, which enters the exchanger at 10 MPa and 49°C(enthalpy is 176.38 kJ/kg) and leaves at the same pressure as a saturated vapor (enthalpy is 2724.7 kJ/kg). The mass flow rate of sodium is 10,000 kg/h, and its specific heat is constant at L25J/(g)(°C). Determine the mass flow rate of water evaporated in the heat exchanger, in kg/h, and the heat-transfer rate between the two fluids, in kJ/h. (15%)

6.A gearbox operating at steady state receives 20 horsepower along its input shaft，delivers power along its output shaft，and is cooled on its outer surface according to Q = - h A (Tb - T0 )，where =110°F is the temperature of the outer surface and T。= 40°F is the temperature of the surroundings far from the gearbox. The product of the heat transfer coefficient h and outer surface area A is 35 Btu/h*R. For the gearbox, determine the power delivered along the output shaft，the rate of availability transfer accompanying heat， and the irreversibility rate, each in Btu/h. Express each quantity as a percentage of the input power.

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(1)