Chapter 5, Problem 5.26P

A system executes a power cycle while receiving 1000 Btu by heat transfer at a temperature of 900°R and discharging 700 Btu by heat transfer at a temperature of 540°R. There are no other heat transfers. Determine the cycle thermal efficiency. Use the Clausius Inequality to determine  σ cycle  in Btu/°R. Determine if this cycle is internally reversible, irreversible, or impossible.

A heat pump cycle is used to maintain the interior of a building at 25°C. At steady state, the heat pump receives energy by heat transfer from well water at 9°C and discharges energy by heat transfer to the building at a rate of 120,000 kJ/h. Over a period of 14 days, an electric meter records that 1500 kW · h of electricity is provided to the heat pump.Determine:(a) the amount of energy that the heat pump receives over the 14-day period from the well water by heat transfer, in kJ.(b) the heat pump’s coefficient of performance.(c) the coefficient of performance of a reversible heat pump cycle operating between hot and cold reservoirs at 25°C and 9°C.

As shown in the figure below, two reversible cycles arranged in series each produce the same net work, Wcycle. The first cycle receives energy QH by heat transfer from a hot reservoir at TH-1000°R and rejects energy Q by heat transfer to a reservoir at an intermediate temperature, T. The second cycle receives energy Q by heat transfer from the reservoir at temperature T and rejects energy Qc by heat transfer to a reservoir at Te - 500°R. All energy transfers are positive in the directions of the arrows. Determine: Hot reservoir at TH lH R1 Reservoir Q at T 20 R2 lc Cold reservoir at Tc We cycle W Wcycle (a) the intermediate temperature T, in °R, and the thermal efficiency for each of the two power cycles. (b) the thermal efficiency of a single reversible power cycle operating between hot and cold reservoirs at 1000°R and 500°R, respectively. Also, determine the ratio of the network developed by the single cycle to the network developed by each of the two cycles, Wcycle-

Two kilograms of air within a piston–cylinder assembly executes a Carnot power cycle with maximum and minimum temperatures of 700 K and 300 K, respectively. The heat transfer to the air during the isothermal expansion is 60 kJ. At the end of the isothermal expansion the volume is 0.4 m3. Assume the ideal gas model for the air. Determine the thermal efficiency, the volume at the beginning of the isothermal expansion, in m3, and the work during the adiabatic expansion, in kJ.

The refrigerator shown in the figure below operates at steady state with a coefficient of performance (COP) of 5.0 within a kitchen at 23 °C. The refrigerator rejects 4.8 kW by heat transfer to its surroundings from metal coils located on its exterior. Determine: (a) the power input, in kW.(b) the lowest theoretical temperature inside the refrigerator, in K.

A closed system loses energy by heat transfer at the rate of 10KJ/s. If the system operates at steady state, explain whether work was done on the system or by the system.

A reversible power cycle whose thermal efficiency is 50% operates between a reservoir at 1800 K and a reservoir at a lower temperature T. Determine T, in K.

Two kilograms of air within a piston-cylinder assembly execute a Carnot power cycle with maximum and minimum temperatures of 750 K and 300 K, respectively. The heat transfer to the air during the isothermal expansion is 60 kJ. At the end of the isothermal expansion the volume is 0.4 m³. Assuming the ideal gas model for the air, determine (a) the thermal efficiency. (b) the pressure and volume at the beginning of the isothermal expansion, in kPa and m3, respectively.

As shown in the figure below, two reversible cycles arranged in series each produce the same net work, Wcycle. The first cycle receives energy QH by heat transfer from a hot reservoir at TH = 1500°R and rejects energy Q by heat transfer to a reservoir at an intermediate temperature, T. The second cycle receives energy Q by heat transfer from the reservoir at temperature T and rejects energy QC by heat transfer to a reservoir at TC = 450°R. All energy transfers are positive in the directions of the arrows.   Determine:(a) the intermediate temperature T, in °R, and the thermal efficiency for each of the two power cycles.(b) the thermal efficiency of a single reversible power cycle operating between hot and cold reservoirs at 1500°R and 450°R, respectively. Also, determine the ratio of the net work developed by the single cycle to the net work developed by each of the two cycles, Wcycle.