Answer:
<em>a) efficiency is equal to 67.2%, and this is lesser than the maximum obtainable efficiency, so this power output is possible.</em>
<em>b) efficiency is 75%, this is approximately equal to the maximum obtainable efficiency, but not more that it. This power output is also possible.</em>
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Explanation:
Cold reservoir temperature Tc = 295 K
Hot reservoir temperature Th = 1175 K
Energy input Q = 150000 K/h
Converting to kJ/s, Q = 150000/3600 = 41.66 kJ/s
Maximum efficiency that can be obtained from this cycle = 
==>
= 0.748 ≅ 75%
also recall that actual cycle efficiency = 
Where W is the energy output or work
a) for work of 28 kW,
eff =
=
= 0.672 ≅ 67.2%
this is lesser than the maximum obtainable efficiency, so this power output is possible.
b) for work of 31.2 kW
eff =
=
= 0.748 ≅ 75%
this is approximately equal to the maximum obtainable efficiency, but not more that it. This power output is possible.
NB: kW is also equal to kJ/S