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

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 = $1 - \frac{Tc}{Th}$

==> $1 - \frac{295}{1175}$ = 0.748 ≅ 75%

also recall that actual cycle efficiency = $\frac{W}{Q}$

Where W is the energy output or work

a) for work of 28 kW,

eff =  $\frac{W}{Q}$ =  $\frac{28}{41.66}$ = 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 =  $\frac{W}{Q}$ =  $\frac{31.2}{41.66}$ = 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