A photovoltaic solar collector with an area of 2 m2 is tracking the sun for 8 hours on a sunny day. Assume that, the solar flux on the collector is constant through the day as 1000W/m2. PV Solar collector properties are:

FF: %75, Efficiency: %18.2

V (MPP, nominal) = 28 V

V (Open Circuit) = 32 V

a) What is the total amount of energy converted to electricity?

b) Assume a reasonable price for the cost of electricity and then calculate the value of electricity ($) produced for whole day.

c) Calculate the generated current and Short Circuit Current.

Question:1

Calculate the density, in g/cm³, of a metal that has a volume of 41.3 L and a mass of 70.05 kg.

Question:2

You have 20.0 L of a 8.18% by volume (% v/v), water-based dye solution. Calculate the volume of pure dye and water that were used to prepare the solution. You may assume that volumes are additive.

Question:3

How many mL of pure (100.0%) food dye are needed to prepare 437.4 mL of 34.8% by volume (%v/v) food dye solution? You may assume that volumes are additive.

1. A CSTR and a PFR of equal volume (VCSTR = VPFR = V) are used to degrade a compound in a first-order manner under steady-state conditions.

(a) If the CSTR gives a 80% degradation what is the efficiency of the PFR?

(b) If instead of one CSTR of volume V, you use 5 CSTRs in series, each having a volume of 0.2V, what would be the overall degradation efficiency?

(c) Show that the overall efficiency will be equal to that of the PFR (volume V) if you use an infinite number (n→∞) of CSTRs in series each having a volume of V/n.

A 24-mH inductor, an 8.1-Ω resistor, and a 5.9-V battery are connected in series as in the figure below. The switch is closed at t = 0. A circuit contains a battery, a switch, an inductor, and a resistor. The circuit starts at the positive terminal of the battery labeled emf ℰ, goes through the switch labeled S, goes through the inductor labeled L, goes through the resistor labeled R and ends at the negative terminal of the battery. 

(a) Find the voltage drop across the resistor at t = 0. V 

(b) Find the voltage drop across the resistor after one time constant has passed. V 

(c) Find the voltage drop across the inductor at t = 0. V 

(d) Find the voltage drop across the inductor after one time constant has elapsed. V

1) Contract Law - Insurance

Mario has purchased a new kart, and would like to get some insurance on it. The kart is

worth $1,000, and there is a 10% chance he will be in an accident and do $500 worth of

damage to his kart. Mario's utility function is U(V) = ln(V), where V is the value of his

kart.

a) Calculate Mario's expected utility with no insurance.

b) Now suppose Mario can buy auto insurance from Yoshi for a premium of $I that will completely compensate him for his $500 loss if it occurs. Find an expression Mario's

expected utility with insurance.

c) What is the most Mario is willing to pay for insurance?

d) Repeat steps a) - c) with a utility function of U(V) = V. Comment on why any differences are present in willingness to pay for insurance.

1. Prepare a summary of 150-250 words after watching video resources related to coordinate system, map projection and datum

Coordinate Map Projection-Video Resources

Note: For your ease and to avoid cumbersome downloading activity due to internet connectivity, I have chosen these video tutorials explaining different concepts. Please watch these as a part of your lecture notes.

Map Projections Explained - A Beginners Guide

https://www.youtube.com/watch?v=wlfLW1j05Dg

Introducing Coordinate Systems and Map Projections

https://www.youtube.com/watch?v=PICwxT0fTHQ

Map Projections

https://www.youtube.com/watch?v=nJ5r4HJMrfo

Everything you would want to know about Map Projections!

https://www.youtube.com/watch?v=dHT0ckOfScU

Different map projections

https://www.youtube.com/watch?v=qM87BDtXSSQ

A force F = −F0 e ^−x/λ (where F0 and λ are positive constants) acts on a particle of mass m that is initially at x = x0 and moving with velocity v0 (> 0). Show that the velocity of the particle is given by

v(x)=(v0^2+(2F0λ /m)((e^-x/λ)-1))^1/2

where the upper (lower) sign corresponds to the motion in the positive (negative) x direction. Consider first the upper sign. For simplicity, define ve=(2F0 λ /m)^1/2 then show that the asymptotic velocity (limiting velocity as x → ∞) is given by v∞=(v0^2-ve^2)^1/2 Note that v∞ exists if v0 ≥ ve.Sketch the graph of v(x) in this case. Analyse the problem when v0 < ve by taking into account of the lower sign in the above solution. Sketch the graph of v(x) in this case. Show that the particle comes to rest (v(x) = 0) at a finite value of x given by xm=−λ ln(1-v0^2/ve^2)

1. Boltzmann statistics are used to find the distribution or distribution of the velocity of Inert gas at any temperature. If D (v) is the velocity distribution of inert gas at T, then the probability that atoms (or Molecules) of inert gas have velocity in the dv range is equal to D (v) dv, where
D (v) dv = 4π (m / 2πkT) ^ 3⁄2 (v ^ 2) e ^ (- mv2⁄2kT) dv

2.1 Draw the graph between D (v) and v when the inert gas has a temperature of 1000 K (Recommended: Use a program such as Mathematica) to explain. Graph style
2.2 In the Thermosphere atmosphere, which is 100 - 150 km above the earth, the temperature is around 1000 K. Find the probability
Is that the nitrogen gas molecules will escape from gravity. In which the molecules must be faster than the velocity From the earth's surface, which is equal to 11 km / s (recommended: for integration D (v) dv, use the program For example Mathematica)
2.3 The lunar surface velocity is 2.4 km / s. Find the probability that the nitrogen gas molecules will escape from the force. Gravity of the moon And explain that Why does the moon have no atmosphere? (Recommended: set the temperature of the moon's surface to equal1000 K)

5. Prove the Following:

a. Let {v1, . . . , vn} be a finite collection of vectors in a vector space V and suppose that it is not a linearly independent set.

i. Show that one can find a vector w ∈ {v1, . . . , vn} such that w ∈ Span(S) for S := {v1, . . . , vn} \ {w}. Conclude that Span(S) = Span(v1, . . . , vn).

ii. Suppose T ⊂ {v1, . . . , vn} is known to be a linearly independent subset. Argue that the vector w from the previous part can be chosen from the set {v1, . . . , vn} \ T.

b. Let V be a vector space and v ∈ V a vector in it. Argue that the set {v} is a linearly independent set if and only if v 6= ~0. Then use this fact together with part i of part a to prove that if {v1, . . . , vn} is any finite subset of V containing at least one non-zero vector, you can obtain a basis of Span(v1, . . . , vn) by simply discarding some of the vectors vi from the set {v1, . . . , vn}.

c. Suppose {v1, . . . , vn} is a linearly independent set in V and that {w1, . . . , wm} is a spanning set in V.

i. Prove that n ≤ m. Hint: use part ii of part a to argue that, for any r ≤ min(m, n), there is a subset T ⊂ {w1, . . . , wm} of size r such that {v1, . . . , vr , w1, . . . , wm} \ T is a spanning set. Then consider the two possibilities when r = min(m, n).

ii. Conclude that if a vector space has a finite spanning set, then any two bases are finite of equal length. (Necessarily, this means that our notion of dimension from class is well-defined and any vector space with a finite spanning set hence has finite dimension).

1. What is the difference between toxic hunger and true hunger?
2. Briefly explain why everyone is a food addict?
3. What are the symptoms of true hunger?
4. Why do people feel sick temporarily after giving up a toxic diet and how is this related to inflammation?
5. Briefly explain why people argue that diets fail.
6. What is the problem with high-protein diets?
7. What does the author state comprises a diet of nutritional excellence?