Chapter 7, Problem 7.33CU

Shown in Fig. P2.87 is 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 Qout. Of this, 70 MW is provided FMKK-YZSS to the community for water heating and the remainder discarded to the environment without use. The electricity is valued at $0.08 per kW h. If the cycle thermal efficiency is 40%, determine the (a) rate energy is added by heat transfer, Q, in MW, (b) rate energy is discarded to the environment, in MW, and (c) value of the electricity generated, in $ per year. Welec =80 MW Power plant n=40

In your own words, define efficiency as it applies to a device designed to perform an energy transformation.

A closed system undergoes a thermodynamic cycle with 2 steps: process 1-2 (from state 1 to state 2), process 2-1 (from state 2 to state 1). During process 1-2, the system received energy by heat transfer of 25J. During process 2-1, energy was transferred from the system to its surrounding by heat transfer of 15J. This is a power cycle. True or false?

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 Q 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 kWh. If the cycle thermal efficiency is 40 %, determine the i. rate energy is added by heat transfer, Q in MW rate energy is discarded to the environment, in MW value of the electricity generated, in $ per year ii. ii.

2. A thermal machine operates in a carnot cycle between temperatures 820 ° C and 18 ° C. Calculate for each kw of net power that yields: a) The amount of heat that is supplied and discharged in kj/h and b) thermal efficiency.

Define Renewable energies such as wind are called “green energy” since they emit no pollutants or greenhouse gases.

A system undergoes a refrigeration cycle while receiving Qc by heat transfer at temperature Tc and discharging energy Qu by heat transfer at a higher temperature TH. There are no other heat transfers. (a) Using energy and exergy balances, show that the net work input to the cycle cannot be zero. (b) Show that the coefficient of performance of the cycle can be expressed as: Tc TH – TeA'¯ T(Qn – Q). B = where E, is the exergy destruction and To is the temperature of the exergy reference environment. (c) Using the result of part (b), obtain an expression for the maximum theoretical value for the coefficient of performance.

Steady-state operating data are shown in the figure below for an open feedwater heater. Heat transfer from the feedwater heater to its surroundings occurs at an average outer surface temperature of 50°C at a rate of 100 kW. Ignore the effects of motion and gravity and let To = 25°C, po = 1 bar. Determine (a) the ratio of the incoming mass flow rates, m/ṁ2. (b) the rate of exergy destruction, in kW. P2 = 1 bar Tz = 400°C 1 ṁy = 0.7 kg/s Pi = 1 bar T, = 40°C Feedwater heater X3 = 25% P3 = 1 bar Tp = 50°C %3D 2)

7.58 Figure PZ.58 shows a gas turbine power plant using air as the working fluid. The accompanying table gives steady-state operating data. Air can be modeled as an ideal gas. Stray heat transfer and the effects of motion and gravity can be ignored Let To 290 K, po = 100 kPa. Determine, each in kJ per kg of air flowing, (a) the net power developed, (b) the net exergy increase of the air passing through the heat exchanger, (eg- e), and (c) a full exergy accounting based on the exergy supplied to the plant found in part (b). Comment. State p(kPa) T(K) h(kJ/kg) s° (kJ/kg K) 1100 290 290.16 1.6680 500 505 508.17 2 2.2297 3 500 875 904.99 2.8170 4 100 635 643.93 2.4688 a o is the variable appearing in Eq. 6.20a and Table A-22. Heat exchanger Compressor Turbine FIGURE P7.58