The purpose of this differential heating lab is to see which of the given materials would heat up faster or remain the same when heated by our heat lamp. in previous years, when this lab has been conducted for the most part, results were the same as our results. Our background knowledge consisted of knowing about which of the given materials were more flammable.

Hypothesis: if differential heating occurs, then different materials will heat at different rates. I would assume that the leaves would heat up the fastest because i think that the leaves would be the most flammable out of all the other materials. I think the water temp would stay the same because water is less flammable and generally takes a long time to heat up.

Materials: 6 beakers 6 thermometers light source sand dirt tape water bark dust ring stand gravel leaves
Procedure: first we filled each of the six beakers half full with the six different materials provided. Then we placed a thermometer 1/2 way into each beaker with the materials. Then we taped a thermometer to each of the beakers so the thermometer stays in the middle of the beaker. Next we placed all of the beakers directly under the light source and then turned the light source on. Afterwards, we recorded the temperature of each material every three minutes for eighteen minutes total. After the eighteen minutes, we turned the light off but remained recording temperatures every three minutes as the materials cooled for eighteen more minutes. After we finished recording our data we prepared a line graph of temperatures for each material over the thirty six minute time period of heating and cooling.

Data: Data Chart

Conclusion: My hypothesis was correct in saying that the temperature of the water would stay the same while the other materials temperature changed while heating and cooling. i was surprised to find that sand didn’t heat up the fastest since it is usually so hot to walk on during the day...

...evaluating? Yes, I have included a clear description of a geothermal heating system.
2. Does my thesis clearly state my opinion of the subject I am evaluating? Yes, my opinion is that this type of heating system is sought by some homeowners.
3. Have I used effective criteria to evaluate my subject? I believe that my criterion is effective in evaluating my product.
4. Have I made a clear and fair judgment about each evaluative criterion? I think my judgment that this product although expensive, will benefit the homeowner after a couple of years.
5. Have I supported each judgment with specific details and examples? I have used good supporting examples and details for my judgment of this product.
6. Have I ended with an effective conclusion? I believe that my conclusion to this paper is a good summary of my writing.
7. Have I proofread thoroughly? I have proof read my document using the techniques found in my weekly readings and I hope I have not missed something.
Darrell Puehler
Shelly Gussis
English 101
08 February 2013
Geothermal Heating
In today’s economy, the individual homeowner is looking for alternative heat sources in order to save on the high-energy costs of heating a home. Many alternatives have been used. However, over the past twenty years, some homeowners have turned to just one of those alternative heating sources, and that heating source is...

...To: The Honorable Winona I. Zard, Mayor of Emerald City
From: Thinh Quang Le, Home Heating Consultant, Queen Anne Office Natural Habitat
Date: February 24, 2012
Subject: Informative Report on Colin Sell's Home Improvement with Home Heating
On January 18, 2012, Mr. Sell sent a letter to inform us about the condition of his house and ask us whether a consultation for upgrading his house would be beneficial. We replied to him on January 24, 2012, that he would benefit from our consultation, so Mr. Sell agreed to have a consultation and let us examine his home to make a consultation more accurate. After examining his house on February 12, 2012, we recognized that there is no heating system or water heating for the basement and the attic, the boiler and the water radiators are very old and broken.
According to the U.S Department of Energy, Americans have to pay almost $1300 for their energy bills each year while "Heating and cooling account for about 56% of the energy use in a typical U.S. home, making it the largest energy expense for most homes." Therefore, installing one of the latest home heating systems is entirely essential to improving the home environment and saving energy efficiently.
The following informative report will provide the options to improve Mr. Sell's house in order to satisfy cost-effectiveness, environmental friendliness but still...

...Doctor Gary Hall
Differential Equations
March 2013
Differential Equations in Mechanical Engineering
Often times college students question the courses they are required to take and the relevance they have to their intended career. As engineers and scientists we are taught, and even “wired” in a way, to question things through-out our lives. We question the way things work, such as the way the shocks in our car work to give us a smooth ride back and forth to school, or what really happens to an object as it falls through the air, even how that people can predict an approximate future population. These questions, and many more, can be answered and explained through different variations of differential equations. By explaining and answering even just one of these questions through different differential equations I will also be answering two other important questions. Why is differential equations required for many students and how does it apply in the career of a mechanical engineer?
First some background. What is a differential equation?
A differential equation is a mathematical statement that contains one or more derivatives. It states a relationship involving the rates of change of continuously changing quantities modeled by functions. They are used whenever a rate of change is known but the process
giving rise to it is not. The solution of a...

...Dated 17.01.2011
1806 words Manish Kumar
A write up on Solar Water Heating System & JNNSM in India
Introduction
Solar energy, being abundant and widespread in its availability, makes it one of the most attractive sources of energies. Tapping this energy will not only help in bridging the gap between demand and supply of electricity but also save money in the long run. A 100-litre capacity Solar Water Heating System (SWHS) can replace an electric geyser for residential use and may save approximately 1500 units of electricity, annually, under Indian conditions. It has also been estimated that a 100 litre per day (lpd) system (2 m2 of collector area) installed in an industry cans save close to 140 litres of diesel in a year. Based on the above equivalence (100 lpd system saves 1500 units of electricity), it is estimated that in generating the same amount of electricity from a coal based power plant, 1.5 tonnes of CO2 is released into atmosphere annually. One million SWHS installed in homes will, therefore, result in reduction of 1.5 million tonnes of CO2 emission into the atmosphere.
About JNNSM
The Jawaharlal Nehru National Solar Mission (JNNSM) is a major initiative of the Government of India and State Governments to promote ecologically sustainable growth while addressing India’s energy security challenge. It will also constitute a major contribution by India to the global effort to meet the challenges of...

...CHAPTER 2
FIRST ORDER DIFFERENTIAL EQUATIONS
2.1 Separable Variables
2.2 Exact Equations
2.2.1 Equations Reducible to Exact Form.
2.3 Linear Equations
4. Solutions by Substitutions
2.4.1 Homogenous Equations
2.4.2 Bernoulli’s Equation
2.5 Exercises
In this chapter we describe procedures for solving 4 types of differential equations of first order, namely, the class of differential equations of first order where variables x and y can be separated, the class of exact equations (equation (2.3) is to be satisfied by the coefficients of dx and dy, the class of linear differential equations having a standard form (2.7) and the class of those differential equations of first order which can be reduced to separable differential equations or standard linear form by appropriate.
2.1 Separable Variables
Definition 2.1: A first order differential equation of the form
[pic]
is called separable or to have separable variables.
Method or Procedure for solving separable differential equations
(i) If h(y) = 1, then
[pic]
or dy = g(x) dx
Integrating both sides we get
[pic]
or [pic]
where c is the constant of integral
We can write
[pic]
where G(x) is an anti-derivative (indefinite integral) of g(x)
(ii) Let [pic]
where [pic],
that is f(x,y) can be written as the...

...Heating effect of electricity
Energy exists in various forms such as mechanical energy, heat energy, chemical energy, electrical energy, light energy and nuclear energy. According to the law of conservation of energy, energy can be transformed from one form to another.
In our daily life we use many devices where the electrical energy is converted into heat energy, light energy, chemical energy or mechanical energy. When an electric current is passed through a metallic wire like filament of an electric heater, oven or geyser, the filament gets heated up and here electrical energy is converted into heat energy. This is known as 'heating effect of current'.
It is a matter of common experience that a wire gets heated up when electric current flows through it. Why does this happen? A metallic conductor has a large number of free electrons in it. When a potential difference is applied across the ends of a metallic wire, the free electrons begin to drift from the low potential to the high potential region. These electrons collide with the positive ions (the atoms which have lost their electrons). In these collisions, energy of the electrons is transferred to the positive ions and they begin to vibrate more violently. As a result, heat is produced. Greater the number of electrons flowing per second, greater will be the rate of collisions and hence more heat is produced.
1. Mathematical Expression for Heat Produced
2. Application of the...

...Diagonally Implicit Block Backward Differentiation Formulas for Solving Ordinary Differential Equations
1.0 Introduction
In mathematics, if y is a function of x, then an equation that involves x, y and one or more derivatives of y with respect to x is called an ordinary differential equation (ODE). The ODEs which do not have additive solutions are non-linear, and finding the solutions is much more sophisticated because it is rarely possible to represent them by elementary function in close form. In addition, the ODEs is use to solve many problems in real life such as cooling or warming law, radio-active decay, carbon dating and in social issue like predator-prey models and exponential growth model.
In this proposal, we are concerned with the numerical solution of initial value problem (IVP) with two fixed points for ODE. The general form is
y'=(y-v1)(y-v2)gy, (1)
given initial values yxn=yn, where v1<v2 ϵ R and g(y)≠0 is a bounded real-valued function with continuous derivatives. Assume the fixed points are y1x=0 and y2(x)=1.
Diagonally Implicit Two-point Block Backward Differentiation Formulas (DI2BBDF) is a new method from the continuation of the previous methods. One of the methods is block method which is used to compute k blocks and to calculate the current block where each block contain r points. The general form for r point k block is
j=0kAjyn+j=hj=0kBjfn+j,...