Question

A power cycle operates between hot and cold reservoirs at 500 K and 310 K, respectively. At steady state, the cycle rejects energy by heat transfer to the cold reservoir at a rate of 16 MW. Determine the maximum theoretical power that might be developed by such a cycle, in MW.

Answer 1

Maximum theoretical power (output) = 9.80 W

Step-by-step explanation:

The efficiency of power is given by:

η =
`1 - (T_H)/(T_H)` =
`(T_H - T_C)/(T_H)`

Where
`T_H` is temperature of hot reservoir and
`T_C` is temperature of cold reservoir.

given:

`T_H` = 500 K

`T_C` = 310 K

The efficiency of power cycle

η =
`(500 K - 310 K)/(500 K)`

η =
`(190 K)/(500 K)`

η = 0.38

Efficiency in terms of heat rejected and heat transferred to power cycle is as follows

η =
`1 - (Q_(rejected))/(Q_(transferred))`

known that: η = 0.38 and
`Q_(rejected)` = 16 MW

0.38 =
`1 - (16 MW)/(Q_(transferred))`

`(16 MW)/(Q_(transferred))` = 1 - 0.38

`(16 MW)/(Q_(transferred))` = 0.62

`Q_(transferred)` = 25.80 MW

W =
`Q_(transferred)` -
`Q_(rejected)`

W = 25.80 MW - 16 MW

W = 9.80 MW

Answer 2

Maximum theoretical power=16(500-310)=3040 MW