(Solved):   The preliminary design of a space station calls for a power   cycle that at steady sta ...

 

The preliminary design of a space station calls for a power   cycle that at steady state receives energy by heat transfer at   TH= 600 K from a nuclear source and rejects energy to space   by thermal radiation according to Eq. 2.33. For the radiative
surface, the temperature is TC, the emissivity is 0.6, and the   surface receives no radiation from any source. The thermal efficiency of the power cycle is one-half that of a reversible
power cycle operating between reservoirs at TH and TC.
(a) For TC= 400 K, determine Wcycle/A, the net power developed per unit of radiator surface area, in kW/m2 , and   the thermal efficiency.
(b) Plot Wcycle/A and the thermal efficiency versus TC, and determine the maximum value of Wcycle/A.
(c) Determine the range of temperatures TC, in K, for which Wcycle/A is within 2 percent of the maximum value obtained in part (b).
The Stefan-Boltzmann constant is 5.67x10^-8 W/m²K4

5.32 The preliminary design of a space station calls for a power cycle that at steady state receives energy by heat transfer at TH= 600 K from a nuclear source and rejects energy to space by thermal radiation according to Eq. 2.33. For the radiative surface, the temperature is Tc, the emissivity is 0.6, and the surface receives no radiation from any source. The thermal ef- ficiency of the power cycle is one-half that of a reversible power cycle operating between reservoirs at TH and Tc. (a) For Tc = 400 K, determine Weycle/A, the net power de- veloped per unit of radiator surface area, in kW/m², and the thermal efficiency. (b) Plot Wcycle/A and the thermal efficiency versus Tc, and de- termine the maximum value of Wcycle /A. (c) Determine the range of temperatures Tc, in K, for which Wcycle/A is within 2 percent of the maximum value ob- tained in part (b). The Stefan-Boltzmann constant is 5.67 × 10-8 W/m². Kª.