Shown in Fig. P2.87 is a cogeneration power plant

Chapter 2, Problem 2.87

(choose chapter or problem)

Shown in Fig. P2.87 is a cogeneration power plant operating in a thermodynamic cycle at steady state. The plant provides electricity to a community at a rate of 80 MW. The energy discharged from the power plant by heat transfer is denoted on the figure by \(\dot{Q}_{\text {out }}\). Of this, 70 MW is provided

to the community for water heating and the remainder is discarded to the environment without use. The electricity is valued at $0.08 per \(\mathrm{kW} \cdot \mathrm{h}\). If the cycle thermal efficiency is 40%, determine the (a) rate energy is added by heat transfer, \(\dot{Q}_{\text {in }}\), in MW, (b) rate energy is discarded to the environment, in MW, and (c) value of the electricity generated, in $ per year.