In the boiler of a power plant are tubes through which water flows as it is brought from 0.8 MPa, 150°C to 240°C at essentially constant pressure. The total mass flow rate of the water is 100 kg/s. Combustion gases passing over the tubes cool from 1067 to 277 °C at essentially constant pressure. The combustion gases can be modeled as air as an ideal gas. There is no significant heat transfer from the boiler to its surroundings. Assuming steady state and neglecting kinetic and potential energy effects, determine

Let T₀ = 25°C, p₀ = 1 atm.
Round your answers to 3 significant digits.

This is problem 8-7 from El-Wakil’s Powerplant Technology book -- air at 14.696 psia, 40 degF, and with 65 percent relative humidity enters the compressor of a gas turbine cycle. The compressor and turbine have the same pressure ratio of 6 and polytropic efficiencies of 0.8 and 0.9, respectively. Water at 60 degF is injected into the compressor exit air, saturating it. Calculate (a) the air temperature after water injection (b) the percent increase in mass flow rate due to water injection, (c) the compressor work in Btus per pound mass of original air, and (d) the compressor work if water is injected during the compression process to the same temperature as (a), in Btus per pound mass of original air. Use a constant c_p = 0.24 Btu/lb_mdegRankine.

A four-cylinder four-stroke engine is operating at a bmep of 2 bar. The pressure at inlet valve closure is 0.37 bar, and the fmep is 0.8 bar. Assuming that the engine gross indicated efficiency is unchanged, verify that disablement of the valves on two cylinders would reduce the fuel consumption by about 13 per cent compared with about an 8 per cent fuel saving if the fuel was not supplied to two cylinders. Assume that the gross imep is proportional to the pressure at inlet valve closure, and that the gross indicated efficiency is constant. State any additional assumptions that you make. By means of p–V diagram sketches, explain why disabling only the inlet or exhaust valves would have a fuel economy benefit comparable to fuel disablement to two cylinders.

7. Consider the following income-expenditure model of a closed economy. The aggregate consumption function is C = 100 +0.8(Y – T); taxes are T = 380; investment, I, is 300 and government expenditure, G, is 200.

(a) Calculate the multiplier, equilibrium income and the government budget surplus [6 marks]

(b) Now let taxes, T = 10 + 0.25Y. Recalculate the multiplier, equilibrium income and the government budget surplus. Try to explain any differences between your answers and your answers to part (a). [10 marks]

(c) Now we further extend the model and open the economy to trade. Let net exports be NX = 444 - 0.3Y. Keep the tax function as in (b). Recalculate the multiplier and equilibrium income and again explain any differences between your answers and those in part (b).

True or False

On April 9th 2020, the S&P500 was trading at 2,750, implying a current P/E ratio of 18. The expected cash payout ratio (dividends + buybacks) is 92% of earnings (in perpetuity). Analysts’ consensus annual growth forecast in earnings for the index is 3.5% for the next 5 years. Use a risk free rate of 0.8% and set the long term growth rate equal to the risk free rate. 1) Estimate the implied equity risk premium using a two-stage growth model given the current level of the S&P500 index and expectations of cash flows. 2) All else equal (i.e. for a given level of the S&P500 index), what would happen to the iERP if the COVID crisis led investors to lower substantially their expectations of dividends and buybacks? (Would it go up or down?)

A production line operation is tested for filling weight accuracy using the following hypotheses.

Hypothesis       Conclusion and Action
H ₀:  = 16         Filling okay, keep running
H _a:     16       Filling off standard; stop and adjust machine

The sample size is 37 and the population standard deviation is  = 0.8. Use  = .05. Do not round intermediate calculations.

1. What would a Type II error mean in this situation?
   SelectConcluding that the mean filling weight is not 16 ounces when it actually isConcluding that the mean filling weight is 16 ounces when it actually isn'tItem 1
2. What is the probability of making a Type II error when the machine is overfilling by .5 ounces (to 4 decimals)?
   
3. What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)?