Chapter 6, Problem 6.38P

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.

One kg of fluid expands reversibly according to a linear law from 4.2 bar to 1.4 bar. The initial and final volume are 0.004 and 0.02 m² respectively. The fluid then cooled reversibly at constant pressure, and finally compressed reversibly according to a law PV=C back to initial condition of 4.2 bar and 0.004 m². Calculate the work done for each process, the net work done and sketch the cycle on the P-V diagram. (4480, -1120, -1845 &1515 N-m)

A silicon chip measuring 5 mm on a side and 1 mm in thickness is embedded in a ceramic substrate. At steady state, the chip has an electrical power input of 0.425 W. The top surface of the chip is exposed to a coolant whose temperature is 29°C. The heat transfer coefficient for convection between the chip and the coolant is 0.18 kW/m2 K. If heat transfer by conduction between the chip and the substrate is negligible, determine the surface temperature of the chip, in °R.

Q2 In a system, 90 kJ of heat is supplied from state 1 to state 2 by constant volume process. The internal energy at state 1 is 100 kJ. The system rejects 105 kJ of heat from state 2 to state 3 by constant pressure process and 40 kJ of work is done on it. The system is brought back from state 3 to state 1 by a reversible adiabatic process. Calculate the adiabatic work and the values of internal energy at state 2 and state 3

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 Tc = 500°R. All energy transfers are positive in the directions of the arrows. Determine: Hot reservoir at TH QH Reservoir at T R1 lo ali R2 Qc Cold reservoir at Te W. cycle W cycle (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 net work developed by the single cycle to the net work developed by each of the two cycles, Wcycle.

Air enters a nozzle operating at steady-state at 800°R, with a negligible velocity, and exits with a velocity of 1500 ft/s. Heat transfer occurs from the nozzle to the surroundings at a rate of 10 Btu per lbm of air flowing. Determine the temperature at the exit, °R. Assume: o air is an ideal gas, variable specific heats, and o potential energy effects are negligible.

Exercise 5.50 The refrigerator shown in Fig operates at Refrigerator B = 4.5 steady state with a coefficient of performance of 4.5 and a power input of 0.8 kW. Energy is rejected from the refrigerator to the surroundings at 20°C by heat transfer from metal coils whose average surface temperature is 28°C. Surroundings, 20°C - Coils, 28°C Determine (a) the rate energy that is rejected, in kW. (b) the lowest theoretical temperature inside the refrigerator, in K. (c) the maximum theoretical power, in kW, that could be developed by a power cycle operating between the coils and the surroundings. Would you recommend making use of this opportunity for developing power? 0.8 kW 49 Chapler

T-12

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-