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An inventor claims to have developed a power cycle operating between hot and cold reservoirs at 1175 K and 295 K, respectively, that provides a steady-state power output of (a) 28 kW, (b) 31.2 kW, while receiving energy by heat transfer from the hot reservoir at the rate 150,000 kJ/h. Evaluate each claim

Answer :

tochjosh

Answer:

a) efficiency is equal to 67.2%, and this is lesser than the maximum obtainable efficiency, so this power output is possible.

b) efficiency is 75%, this is approximately equal to the maximum obtainable efficiency, but not more that it. This power output is also possible.

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 = [tex]1 - \frac{Tc}{Th}[/tex]

==> [tex]1 - \frac{295}{1175}[/tex] = 0.748 ≅ 75%

also recall that actual cycle efficiency = [tex]\frac{W}{Q}[/tex]

Where W is the energy output or work

a) for work of 28 kW,

eff =  [tex]\frac{W}{Q}[/tex] =  [tex]\frac{28}{41.66}[/tex] = 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 =  [tex]\frac{W}{Q}[/tex] =  [tex]\frac{31.2}{41.66}[/tex] = 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

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