Consider a regenerative vapor power cycle with two feedwater heaters, a closed one and an open one, and reheat. Steam enters the first turbine stage at 12 MPa, $480^{\circ} \mathrm{C},$ and expands to 2 MPa. Some steam is extracted at 2 MPa and fed to the closed feedwater heater. The remainder is reheated at 2 MPa to $440^{\circ} \mathrm{C}$ and then expands through the second-stage turbine to 0.3 MPa, where an additional amount is extracted and fed into the open feedwater heater operating at 0.3 MPa. The steam expanding through the third-stage turbine exits at the condenser pressure of 6 kPa. Feedwater leaves the closed heater at $210^{\circ} \mathrm{C},$ 12 MPa, and condensate exiting as saturated liquid at 2 MPa is trapped into the open feedwater heater. Saturated liquid at 0.3 MPa leaves the open feedwater heater. Assume all pumps and turbine stages operate isentropically. Determine for the cycle a. the heat transfer to the working fluid passing through the steam generator, in kJ per kg of steam entering the first-stage turbine. b. the thermal efficiency. c. the heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per kg of steam entering the first-stage turbine.

Dry air at $32^{\circ} \mathrm{C}$ flows over a wetted (water) plate of $0.2 \mathrm{m}^{2}$ area. The average convection coefficient is $\bar{h}=20 \mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}$, and the heater power required to maintain the plate at a temperature of $27^{\circ} \mathrm{C}$ is 432 W. Estimate the power required to maintain the wetted plate at a temperature of $37^{\circ} \mathrm{C}$ in dry air at $32^{\circ} \mathrm{C}$ if the convection coefficients remain unchanged.

Suppose X and Y are finite sets, X has more elements than Y, and

$$F : X \rightarrow Y$$

is a function. By the pigeonhole principle, there exist elements a and b in X such that

$$a \neq b$$

and F(a)=F(b). Write a computer algorithm to find such a pair of elements a and b.

If x<y, then

$$x < \frac { x + y } { 2 } < y$$

. Use this fact to give a convincing argument for the following: Between any two rational numbers there are infinitely many rational numbers.

An insulated rigid tank contains 4 kg of argon gas at 450 kPa and 30$^\circ{}$C. A valve is now opened, and argon is allowed to escape until the pressure inside drops to 200 kPa. Assuming the argon remaining inside the tank has undergone a reversible, adiabatic process, determine the final mass in the tank. Answer: 2.46 kg

Consider a simple ideal Rankine cycle and an ideal regenerative Rankine cycle with one open feedwater heater. The two cycles are very much alike. except the feedwater in the regenerative cycle is heated by extracting some steam just the regenerative cycle is heated by extracting some steam just before it enters the turbine. How would you compare the efficiencies of these two cycles?

Obtain the steady-state response of each of the following models, and estimate how long it will take the response to reach steady state.a. b. c.

The term regeneration is used to describe the use of regenerative feedwater heaters in vapor power plants and regenerative

Carbon dioxide $(CO_2)$ at $197^\circ C,$ 2 bar enters a chamber at steady state with a molar flow rate of 2 kmol/s and mixes with nitrogen $(N_2)$ entering at $27^\circ C,$ 2 bar with a molar flow rate of 1 kmol/s. Heat transfer from the mixing chamber occurs at an average surface temperature of $127^\circ C.$ A single stream exits the mixing chamber at $127^\circ C,$ 2 bar and passes through a duct, where it cools at constant pressure to $42^\circ C$ through heat transfer with the surroundings at $27^\circ C.$ Kinetic and potential energy effects can be ignored. Determine the rates of heat transfer and exergy destruction, each in kW, for control volumes enclosing a. the mixing chamber only. b. the mixing chamber and enough of the nearby surroundings that heat transfer occurs at $27^\circ C.$ c. the duct and enough of the nearby surroundings that heat transfer occurs at $27^\circ C.$ Let $T_{0}=27^{\circ} \mathrm{C}.$

Solve the equation. Check your solution. d - 10 = 10

Fill in each blank so that the resulting statement is true. The ____ property of multiplication states that ____ can be deleted from a product.

A mixture of 1 kmol of hydrogen $(H_2)$ and n kmol of oxygen $(O_2),$ initially at $25^\circ C$ and 1 atm, burns completely in a closed, rigid, insulated container. The contauier finally holds a mixture of water vapor and $O_2$ at 3000 K. The ideal gas model applies to each mixture and there is no change in kinetic or potential energy between the initial and final states. Determine a. the value of n. b. the final pressure, in atm.

Graph the function

$$y = \frac { 10 } { x }$$

What are the domain, range, and asymptotes of the function?

At the beginning of the compression process of an air-standard Diesel cycle, $P_1 = 95 kPa$ and $T_1 = 300 K.$ The maximum temperature is 1800 K and the mass of air is 12 g. For compression ratios of 15, 18, and 21, determine the net work developed, in kJ, the thermal efficiency, and the mean effective pressure, in kPa.