A well mixed 10m³ closed mixing tank at 18C is used to dilute 100kg/min of a 2.0% by mass NaClO₃ solution to a 0.60% solution by adding water.

Part 1) What is the mass flowrate of water into the tank needed at steady-state to accomplish this dilution?

Part 2) You notice that some gas bubbles appear in the effluent, and after some additional literature reading, hypothesize that NaCl₃ is decomposing to NaCl and O₂ inside the tank because of impurities in its walls. You do not have an oxygen detector handy and so decide to build a 0.5m³ chamber above the tank to collect all the gas generated. Initially the pressure (absolute) in this collection chamber is 760mmHg. After five minutes you measure the pressure to be 1320mmHg.

a) if your hypothesis is correct, what is the mass rate of oxygen generation?

b) assuming that the NaCl₃ solution flowing in and the NaCl₃/NaCl solution flowing out each have a density of 1.0g/mL (which will be within 1% of truth), what is the concentration (g/L) of NaCl in the effluent?

c) if a portion of water from the effluent were evaporated without any additional decomposition occuring, what would be the purity of the NaClO₃?

d) after more literature reading, you believe that the rate of  NaClO₃ decomposition is directly proportional to the molar concentration of  NaClO₃ in the tank and the tank volume, Based on this hypothesis, determine the value of the proportionality constant, thereby obtaining a general expression for the rate of  NaClO₃ decomposition.

Part 3) The dilution water has been flowing and the  NaClO₃ decomposing at steady state rate. suddenly, the valve controlling the flow of dilution water malfunctions and closes, halting its flow. assuming the densities of all the solutions are approximately the same, how much time passes before the concentration of  NaClO₃ in the effluent exceeds 1%?

2. Consider a domestic closed market (no international trade) with the following demand and supply functions:

P = 150 − 1/2Q

P=Q
(a) Calculate the domestic equilibrium price and quantity

(b) Calculate the consumer surplus and the producer surplus

(c) Suppose the domestic country decides to open up its markets and begins international trade. The world price (Pw) is $30 lower than the former domestic equilibrium price. How much quantity is now supplied by the domes- tic producers in the market? (QDomestic) How much quantity is imported from international producers in the market? (QImport). You must show work.

(d) (What is the new consumer surplus and producer surplus?

(e) Who benefited from opening up the market (Domestic consumers? Domestic producers?)

(f) (2 points) Did the domestic market efficiency improve?

Assume a closed economy without Government. However, there exists a financial sector that creates an array of financial assets on which both households and firms invest.

Let ? denote the average earnings from these financial assets. The consumption expenditure of the households is influenced by their wage income and the financial income and is given by ? = ?(?, ?); ?? > 0, ?? > 0, where ??, ?? are partial derivatives of consumption with respect to income ? and financial earnings ? respectively. Similarly, the real investment expenditure of firms is given by ? = ?(?, ?); ?? > 0, ?? < 0, where ??, ?? are the partial derivatives of the real investment with respect to income and financial earnings. Using either the Keynesian cross model or the Multiplier analysis, answer the following questions.

(i) Derive the relationship between output ? and financial earnings ?, and examine the analytical conditions under which the relationship is positive ( ?? ?? > 0) and negative ( ?? ?? < 0).

(ii) Describe why the scenario where the expansion in output driven by the rise in financial earnings, i.e. when ?? ?? > 0, could make the economy unstable and vulnerable to crisis?

Find a closed formula for each of the following sequences. Show all work and explain your answers.

(a) {1, 6, 17, 34, 57, 86, 121, . . .}, where a₀ = 1.

(b) a_n = 5a_n−1 + 4, a₀ = 2

(c) a_n = 10a_n−1 − 21a_n−2, a₀ = 6, a₁ = 26.

There are three possibilities for the shape/curvature of the universe: positive curvature (closed), negative curvature (open), and flat curvature. These all imply different things about the ultimate fate of the expanding universe. What kinds of observable tests could cosmologists use to distinguish one curvature from the next? Please write a detailed paragraph explaining what kinds of theory/observations cosmologists would have to make to determine that the universe has negative curvature (open)?

Consider a closed economy where aggregate expenditure is AE = C + I + G. Government purchases (G) is a constant, which do not vary with output level (Y). Consumption (C) is an increasing function of disposable income YD: C = a + bYD. In this economy, we have lump sum tax only; YD = Y –T. Investment is an increasing function of Y: I = k + iY.

1. The equilibrium condition is Y = AE. Solve for the equilibrium Y of the economy.

2. What are the multipliers with respect to the autonomous expenditures (a, k, G) and tax (T)?

3. Solve for the equilibrium disposable income.

4. Solve for the equilibrium consumption.

5. Solve for the equilibrium investment.

6. Solve for the equilibrium private saving (the saving of households) and total saving (private saving + government saving). Is the total saving equal to investment?

7. Do the private saving and total saving vary with autonomous consumption(a) or marginal propensity to consume(b)? If it is the case, how do the private saving and total saving vary with a?

At 4:00 p.m. a closed flask of sterile broth is inoculated with 10,000 cells. The lag phase lasts 1 hour. At 9:00 p.m. the log phase culture has a population of 65 million cells. The mean generation time is approximately

• 10 minutes.

• 40 minutes.

• 20 minutes.

• 30 minutes.

The correct answer is 20 minutes, but can you please show me how to get to this answer?

Assume a closed economy without Government. However, there exists a financial sector that creates an array of financial assets on which both households and firms invest. Let ? denote the average earnings from these financial assets. The consumption expenditure of the households is influenced by their wage income and the financial income and is given by ? = ?(?, ?); ?? > 0, ?? > 0, where ??, ?? are partial derivatives of consumption with respect to income ? and financial earnings ? respectively. Similarly, the real investment expenditure of firms is given by ? = ?(?, ?); ?? > 0, ?? < 0, where ??, ?? are the partial derivatives of the real investment with respect to income and financial earnings. Note that ?? < 0 implies that the real investment falls as financial earnings for the firm rises. Either using the Keynesian cross model or the Multiplier analysis, answer the following questions. (i) Identify the “wealth effect” in this model? [2] (ii) Derive the relationship between output ? and financial earnings ?, and examine the analytical conditions under which the relationship is positive ( ?? ??>0) and negative ( ?? ?? < 0). [15] (iii) Describe why the scenario where the expansion in output driven by rise in financial earnings, i.e. when ?? ??>0, could make the economy unstable and vulnerable to crisis? [8]

A closed-end fund starts the year with a net asset value of $21 . by year-end , NAV equals $20.5 . At the beginning of the year , the fund is selling at a 3% premium to NAV. By the end of the year, the fund is selling at a 4% discount to NAV . the fund paid year-end distributions of income and capital gains of 2.50$ . what is the rate of return to an investor in the fund during the year ?