Assume the following model of the economy, with the price level fixed at 1.0:

C = 0.8(Y – T) i = 1000 – 20r

T = 500

G = 1,000

Ms = 1,000

Md/P = 0.5Y – 50ra

A) What are the short-run equilibrium values of Y, and r.

B) Assume that T decreases by 100. By how much will Y increase in short-run equilibrium?

C) Assume that T is back at its original level of 500, but Ms (money supply) increases by 100. By how much will Y increase in short-run equilibrium?

Calculate the pH of an aqueous solution that is 1.0 M Na2CO3. Ka2 for H2CO3 is 4.7 × 10-11. Please post full work and explanation. Thank you.

1. A pendulum is formed by taking a 1.0 kg mass and hanging it from the ceiling using a steel wire with a diameter of 1.1 mm. It is observed that the wire stretches by 0.05 mm under the weight of the mass. What is the period of oscillation of the pendulum?

2. In order to study the long-term effects of weightlessness, astronauts in space must be weighed (or at least "massed"). One way in which this is done is to seat them in a chair of known mass attached to a spring of known force constant and measure the period of the oscillations of this system. The 34.8 kg chair alone oscillates with a period of 1.45 s , and the period with the astronaut sitting in the chair is 2.25 s .

a.) Find the force constant of the spring.

b.) Find the mass of the astronaut.

a strip of Ag was placed in a beaker containing 1.0 M AgNO3, and a strip of Co was put in a second beaker containing Co(NO3)2. The silver and cobalt electrodes were connected by a wire through an ammeter, and the two beakers were connected by a NaCl salt bridge.

1. Use E0 valuesto describe which way the electrons will flow. Show the direction of electron flow on the diagram, then label the anode and the cathode.Ag+ + e- = Ag (s) E0=0.80;

Co2++2 e- = Co (s) E0=-0.28

2. write and label the oxidation and reduction half-reactions that will be occuring if the electrons are flowing in the direction shown on your diagram. Show the final balanced equation.

3. Use the above 1/2 reaction to find the maximum total E0 valune for the entire cell.

4. Explain in detail what the sodium and chlorine ions in the salt bridge are doing and why they must do this.

5. What happens to the voltage of the cell as equilibrium is approached?

6. What voltage would have to be applied from another battery to make the cell run in reverse?

Consider two gases, A and B, each in a 1.0 L container and each at the same temperature and pressure. The mass of gas A in the container is 0.54 g and the mass of gas B in the container is 0.40 g

a. Which container has more molecules?

b. Which gas sample has the largest average kinetic energy?

c. Which gas sample has the fastest average velocity?

d. The molecules A are larger than B and thus hit the walls with more force, so how can the pressure in the two containers be equal to each other?

A thermocouple junction of 1.0-mm in diameter is inserted in a large chamber to measure the temperature of hot gas flowing through the chamber. The hot gas has a velocity of 2 m/s and temperature (Tg) at 800 K. The chamber surface (Ts) is maintained at 500 K.

(a) If the thermocouple is at room temperature, Ti when it is inserted in the chamber, calculate the time required for the temperature difference, (Tg–T) to reach 2% of the initial temperature difference Tg-Ti . Neglect radiation and conduction through the leads. Properties of the thermocouple junction are approximated as k = 100W/mK, c = 385 J/kgK and  = 8920 kg/m3 , while those of the hot gases may be assumed to have the properties of air at atmospheric pressure.

(b) If the thermocouple junction has an emissivity of 0.5, what is the steady state temperature of the thermocouple junction?

(c) The emissivity of the thermocouple junction can be controlled through application of a thin coating. How would changes in the emissivity affect the temperature measurement error? Compute the steady state junction temperature for emissivities in the range 0.1  ɛ  1. Results are to be presented in graphical and / or tabular forms and should be accompanied by substantial discussion supported by heat transfer fundamentals.

(d) Suggest ways to eliminate the temperature measurement error

A sample of gas has an initial volume of 34.2 L at a pressure of 1.0 atm .

If the sample is compressed to a volume of 14.9 L , what is its pressure?

A spherical motile bacteria with a radius of 1.0 microns and a density approximately equal to water is swimming in water (temperature 20 C) at a speed of 8.0 microns per second. The bacteria suddenly stops swimming. Since the Reynolds number for a swimming bacteria is small, it should experience Stokes drag (F?_D? = 6????Rv).

(a) How long (in seconds) does it take the bacteria to come to a “complete” stop? We’ll define a “complete” stop to be when the speed has dropped to 25.0 nanometers per second.

(b) How far (in meters) does the bacteria coast in this time?

A 1.0 gram sample of an unknown metal was heated to 75 C, and then placed in a calorimeter filled with 100mL of water that had an initial temperature of 26 C. Once the system was allowed to reach thermal equilibrium the temperature of the water was 31 C. what is the specific heat capacity of the metal?

What is the actual concentration of the molecular form of HF in a 1.0 M HF solution given that K_a of HF is 6.8 ´ 10^-4?