Question

Please explain how the answer is obtained and also the work. I want to understand how to solve this problem. Thank you.

A typical coal-fired power plant generates 1000 MW of usable power at an overall thermal efficiency of 38%. The rate of heat input to the plant is 2630MW.

a) The plant burns anthracite coal, which has a heat of combustion of 2.65×107J/kg. How much coal does the plant use per day, if it operates continuously?

b) At what rate is heat ejected into the cool reservoir, which is the nearby river?

c) The river's temperature is 18.0 ∘C before it reaches the power plant and 18.6 ∘C after it has received the plant's waste heat. Calculate the river's flow rate, in cubic meters per second.

d) By how much does the river's entropy increase each second?

Answer 1

The thermal efficiency of a plant is given by P out/P in

P in = P out/0.38 = 1000/0.38 = 2631 MW

a) The energy consumption per day will be 2631 × 10⁶ × 86400

= 2.27 × 10¹⁴ J

Coal comsumed will be 2.27 × 10¹⁴/2.65 × 10⁷ = 8.56 × 10⁶ kg of coal per day will be required.

b) P_waste = P_in - P_out = 2631 MW - 1000 MW = 1631 MW

c) P = mc ∆T/t

m/t = P/c ∆T = 1631 × 10⁶/(4200 × 0.6) = 6.47 × 10⁵ kg/s

d) dS = dQ /T

= m c dT/T

S/t =( m/t) c dT/T

6.47 × 10⁵ × 4200 ( ln 291.5 - ln291)

= 4.66 × 10⁶ J/K.s