A piston–cylinder device contains steam that undergoes a reversible thermodynamic cycle. Initially the steam is at 400 kPa and 350oC with a volume of 0.3 m3. The steam is first expanded isothermally to 150 kPa, then compressed adiabatically to the initial pressure, and finally compressed at the constant pressure to the initial state. Determine (a) the net work and heat transfer for the cycle after you calculate the work and heat interaction for each process and (b) show the cyclic process on a PV diagram

A mass of 0.3 kg of saturated refrigerant-134a is contained in a piston-cylinder device at 240 kPa.
Initially, 70 percent of the mass is in the liquid phase. Now heat is transferred to the refrigerant at
constant pressure until the cylinder contains vapor only.
(a) show the process on a P-v and T-v diagrams with respect to saturation lines. Determine;
(b) the volume occupied by the refrigerant initially,
(c) the work done, and
(d) the total heat transfer.

Fair Dice

We roll a fair dice 10 times and register how many times we obtained 5.

(a) Find the probability to obtain 5 seven times.

(b) Estimate the number of fives that will come out with the probability 0.35.

(c) What is the probability of geting 30 fives when rolling a fair dice 45 times?

(d) How many fives will come out with a probability of 0.25, when rollong a fair dice 45 times?

Recall the general equation for pressure volume work and the equations for the four special cases we have considered; a free expansion, an expansion against constant pressure and a reversible, isothermal expansion of a perfect gas and the adiabatic expansion of a perfect gas. (Even though we say expansions, for all but free expansion processes, the same equations hold for compressions as well.) Give the appropriate equation for calculating work in the following typed problems. These problems came from several different textbooks. Some of these use the term ideal gas instead of perfect gas. Calculate complete answers to problems 3, 4 and 7, and the problem 2.7 found at the end of this document 1. If a balloon filled to a volume of 1.25 L with a perfect gas is placed in a sealed chamber at a constant temperature of 18oC and the pressure in the chamber increased slowly until the balloon is squeezed to 1.00 L how much work is done on the gas in the balloon? 2. A nonideal (non perfect) gas is heated slowly and expands reversibly at a constant pressure of 275 torr from a volume of 385 cm3 to 875 cm3. Find the work in Joules. 3. A balloon 15 m in diameter is inflated with helium at 20oC. How much work is done during inflation against an external pressure of 1 atm. (101325 Pa), from initial volume of zero to its final volume? 4. 1.5 mol of a gas that behaves perfectly was allowed to expand reversibly and isothemrally at 27oC to twice its volume. Calculate w in units of J/mol. 5. A 3.75 mol sample of an ideal gas with CV,m = 3R/2 initially at a temperature Ti = 298 K and pi = 1.00 bar is enclosed in an adiabatic piston and cylinder assembly. The gas is compressed by placing a 725 kg mass on the piston with a diameter of 25.4 cm. Calculate the work done in this process. Assume that the mass of the piston is negligible. 6. The You Tube video found at http://www.youtube.com/watch?v=d4Rz7c0NJSE&feature=related shows a large weather balloon being filled and released from the ground. About 5 minutes into this video the balloon and its payload is free and rising into the atmosphere. The balloon is a bubble of helium gas inside a gas bag much larger than the bubble. You can see this in the wrinkles in the sack and the large amount of fabric hanging below the helium bubble. Atmospheric pressure decreases with elevation as shown below The flexible cloth of the balloon allows the pressure inside and outside of the balloon to remain in equilibrium. Calculate the work done by the expanding gas as the balloon rises from sea level to 5000 m assuming the temperature remains constant. 7. A pellet of Zn of mass 14.5 g is dropped into a flask containing dilute H2SO4 at a pressure of 1.00 bar and 25oC. What is the reaction involved? How much work is done? 8. 2.25 mol of an ideal (perfect) gas at 35.6oC expands isothermally from an initial volume of 26.0 dm3 to a final volume of 40.0 dm3 Calculate the work done A. For an expansion against constant external pressure of 1.00 x 105 Pa B. For a reversible expansion 9.Calculate w for the adiabatic expansion of 1 mole of an ideal (perfect) gas at an initial pressure of 2.25 bar and temperature of 475 K to a final temperature of 322 K. 10. A 1.50 mole sample of an ideal gas initially at 28.5oC expands reversibly and adiabatically from an initial volume of 22.5 dm3 to a final volume of 75.5 dm3. 11. The work done by an engine may depend on its orientation in a gravitational field, because the mass of a piston is relevant when the expansion if vertical. A chemical reaction takes place in a container of cross-sectional area 55.0 cm2; the container has a piston of mass 250 g at one end. As a result of the reaction, the piston is pushed out (a) horizontally, (b) vertically through a distance of 155 cm against an external pressure of 105 kPa. Calculate the work done in each case. 12. A sample of blood plasma occupies 0.550 L at 0oC and 1.03 bar is compressed iso-thermally by 0.57% by being subjected to a constant external pressure of 95.2 bar. Calculate w.

Throughout life, there are “wins” and “losses.” Learning how to cope with loss can affect your health in various ways. For this week’s Discussion topic, you will identify a “loss” situation. This could be a loss of a job, pet, family member, etc.

Discuss how this “loss” could affect a person’s mental health, physical health, and the way they might be thinking about themselves (i.e., self-efficacy). What are ways in which the constructs of self-efficacy theory could be used to help cope with these types of losses? Within this week’s readings, you will find a figure on the self-efficacy theory that may help you formulate a response.

Suppose the management claims that the proportion of games that your team wins when scoring 80 or more points is 0.50. You tested this claim using a 5% level of significance. Explain the steps you took to test this problem and interpret your results.

See Step 5 in the Python script to address the following items:

• In general, how is hypothesis testing used to test claims about a population proportion?
• Summarize all important steps of the hypothesis test. This includes:
  1. Null Hypothesis (statistical notation and its description in words)
  2. Alternative Hypothesis (statistical notation and its description in words)
  3. Level of Significance
  4. Report the Test Statistic and the P-value in a formatted table as shown below:

Table 4: Hypothesis Test for the Population Proportion

• 5. Conclusion of the hypothesis test and its interpretation based on the P-value
• What are the implications of your findings from this hypothesis test? What is its practical significance?

Proportion of games won by your team when scoring more than 80 points in the years 2013 to 2015 = 0.5244
Hypothesis Test for the Population Proportion
Test Statistic = 0.73
P-value = 0.4628

In 20X7, Troy, a resident of Connecticut, wins the Connecticut LOTTO grand prize of $15 million.

The LOTTO contest is governed by the following rules.

The prize is to be paid in 20 equal installments ( in this case, $750,000 per year) with no interest provided for.

The rights to the prize award are not assignable. If a winner dies during the payout period, however, the remaining installment payments are to be made to the winner’s duly appointed executor.

The prize award is not specifically funded or guaranteed by any state agency. It constitutes a general obligation of the state of Connecticut.

Troy dies in 20X9 after having received two payments of $750,000 each. Troy’s estate includes the present value of the remaining $13.5 million prize award in the estate at $4.86 million. This is determined by using the IRS table amount of $6.75 million and discounting it for absence of security ( ie., no separate funding or guarantee of payment by a state agency) and lack of marketability (ie., the award cannot be assigned). The table is be used in valuing, among other income interests, private (ie., noncommercial) annuity contracts.

Upon audit of the estate tax return, the IRS disputes the deviation from the table amount. The IRS argues that the absence-of-security discount is inappropriate because the state of Connecticut has never defaulted on any of its LOTTO obligations. Furthermore, the lack-of-marketability discount is inappropriate applied to annuity-type situations. Unlike stocks and bonds and other ownership interests, private annuities are not subject to marketplace valuation procedures.

Who should prevail? The taxpayer or the IRS.

Do the following:

(1)      Give your opinion. In it, show authorities, citing law, regulations, interpretations and decisions applicable.

(2)      Enumerate and explain every step you take in reaching your result. These are extremely important - just as important as the conclusion itself.

In a 4x4 multistage butterfly network, Pe is the probability that a link is fault-free. write expressions for the bandwidth BW, connectability Q, and the expected number of accessible processors. Assume that a processor generates memory requests with a probability Pr. assume that switchboxes do not fail.

1. Suppose that the probability that a certain experiment will be successful is 0.4, and let X denote the denote the number of successes that are obtained in 15 independent performances of the experiment. What is the probability of getting at least 12 successes experiments? What is the expected value and variance for the described distribution?