Question

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 1

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.

Step-by-step 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 =
`1 - (Tc)/(Th)`

==>
`1 - (295)/(1175)` = 0.748 ≅ 75%

also recall that actual cycle efficiency =
`(W)/(Q)`

Where W is the energy output or work

a) for work of 28 kW,

eff =
`(W)/(Q)` =
`(28)/(41.66)` = 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 =
`(W)/(Q)` =
`(31.2)/(41.66)` = 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