The critical angles for ethyl alcohol, water, and carbon disulfide when surrounded by water are approximately 76.64°, no critical angle, and 54.02°, respectively.
For the light of wavelength 589 nm, to calculate the critical angles for ethyl alcohol, water, and carbon disulfide when surrounded by water, we need to know their refractive indices. The refractive index of water (n1) is approximately 1.33.
1. Ethyl alcohol: Its refractive index (n2) is approximately 1.36. To calculate the critical angle (θc), use Snell's Law:
sin(θc) = n1 / n2
θc = arcsin(n1 / n2) = arcsin(1.33 / 1.36) ≈ 76.64°
2. Water: Since the substance and surrounding medium are both water, there is no critical angle because the refractive indices are the same.
3. Carbon disulfide: Its refractive index (n2) is approximately 1.63. To calculate the critical angle:
θc = arcsin(n1 / n2) = arcsin(1.33 / 1.63) ≈ 54.02°
Thus, the critical angles for ethyl alcohol, water, and carbon disulfide when surrounded by water are approximately 76.64°, no critical angle, and 54.02°, respectively.
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How many moles of iron is 6.022 x 10^22 atoms of iron? (Report answer as a number rounded to one place past the decimal.) *
\(\displaystyle 0.1 \ mol \ Fe\)
General Formulas and Concepts:Math
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightChemistry
Atomic Structure
Avogadro's Number - 6.022 × 10²³ atoms, molecules, formula units, etc.Stoichiometry
Using Dimensional AnalysisExplanation:Step 1: Define
6.022 × 10²² atoms Fe (iron)
Step 2: Identify Conversions
Avogadro's Number
Step 3: Convert
Set up: \(\displaystyle 6.022 \cdot 10^{22} \ atoms \ Fe(\frac{1 \ mol \ Fe}{6.022 \cdot 10^{23} \ atoms \ Fe})\)Divide: \(\displaystyle 0.1 \ mol \ Fe\)systematic evaluation of materials for post-combustion co2 capture in a temperature swing adsorption process
The question is about the systematic evaluation of materials for post-combustion CO2 capture in a temperature swing adsorption process.
In a temperature swing adsorption process for post-combustion CO2 capture, materials are evaluated systematically to determine their effectiveness in capturing CO2. Here is a step-by-step explanation of the process:
1. Material selection: Various materials, such as zeolites, activated carbon, metal-organic frameworks (MOFs), and amine-based sorbents, are considered for CO2 capture. Each material has different properties and adsorption capacities.
2. Screening: The selected materials are screened based on specific criteria, such as CO2 adsorption capacity, selectivity, stability, and cost. This helps narrow down the choices to the most promising candidates.
3. Bench-scale testing: The selected materials undergo bench-scale testing to evaluate their performance under controlled conditions. This involves measuring the CO2 adsorption capacity, kinetics, and regeneration efficiency of each material.
4. Process modeling: Computer simulations are used to model the temperature swing adsorption process with different materials. This helps predict the overall performance of the system, including CO2 capture efficiency, energy requirements, and process optimization.
5. Pilot-scale testing: The most promising materials are then tested at a larger scale in a pilot plant. This helps validate their performance and assess any challenges or limitations that may arise during practical implementation.
6. Techno-economic analysis: The performance data obtained from the pilot-scale testing is used to conduct a techno-economic analysis. This involves evaluating the cost-effectiveness of the materials, including their initial investment, operating costs, and potential for scaling up.
7. Material optimization: Based on the results of the evaluations and analysis, further modifications or improvements can be made to the materials to enhance their performance, stability, or cost-effectiveness.
By following this systematic evaluation process, researchers and engineers can identify the most suitable materials for post-combustion CO2 capture in a temperature swing adsorption process.
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Find the entropy of 1 mole of N2 molecule consider it as an ideal gas occupying a cubic volume of side 1 cm
choices
1: 74 J/K
2: 37
3:136
4: 62
The entropy of 1 mole of N2 molecules, considered as an ideal gas occupying a cubic volume of side 1 cm, is approximately 4: 62 J/K.
To find the entropy of 1 mole of N2 molecules, we need to use the formula for entropy:
S = R * ln(W)
Where:
S is the entropy
R is the gas constant
ln is the natural logarithm
W is the number of microstates or ways the system can be arranged
For an ideal gas, the number of microstates can be calculated using the formula:
W = (V^N) / (N!)
Where:
V is the volume
N is the number of molecules
Given that we have 1 mole of N2 molecules, which is approximately 6.022 x 10^23 molecules, and the volume of the cube is 1 cm^3, we can calculate the entropy.
First, let's convert the volume from cm^3 to m^3:
1 cm^3 = (1 x 10^-2 m)^3 = 1 x 10^-6 m^3
Now, we can substitute the values into the formula for W:
W = ((1 x 10^-6 m^3)^(6.022 x 10^23)) / (6.022 x 10^23)!
To simplify the calculation, we can use the fact that ln(W) is equivalent to ln((V^N) / (N!)) = ln(V^N) - ln(N!).
ln(W) = ln((1 x 10^-6 m^3)^(6.022 x 10^23)) - ln(6.022 x 10^23)!
ln(W) = (6.022 x 10^23) * ln(1 x 10^-6 m^3) - ln(6.022 x 10^23)!
Now, substituting the values of ln(1 x 10^-6 m^3) and ln(6.022 x 10^23) into the equation:
ln(W) = (6.022 x 10^23) * (-13.8155) - ln(6.022 x 10^23)!
Finally, we can use the value of the gas constant, R, which is approximately 8.314 J/(mol·K), to calculate the entropy:
S = R * ln(W) = (8.314 J/(mol·K)) * ((6.022 x 10^23) * (-13.8155) - ln(6.022 x 10^23)!)
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if 53 grams of magnesium oxide reacts with an excess amount of sodium chloride, how many grams of magnesium chkiride wikk ve nade
If 53 grams of magnesium oxide reacts with an excess amount of sodium chloride there would be 125.18 g magnesium chloride
The limiting reactant is magnesium oxide since NaCl is in excess, which MgO has a mass of 53.00 grams.
MgO molar mass is 40.31 g/mol.
MgCl₂'s molar mass is95.211 g/mol
The equation with a balance reaction
2NaCl + MgO → Na2O + MgCl₂
We should determine the moles of MgO
Mass MgO divided by molar mass MgO yields moles of sodium chloride.
moles of MgO = mass/ molar mass
moles of MgO = 53 grams / 40.31 g/mol
moles of MgO = 1.3148 moles
Calculate the moles of Na₂O
MgO is the limiting reactant.
To make 1 mol of Na₂O and 1 mol of MgCl₂ we need 2 moles of NaCl, we require 1 mol of MgO.
with unitary method we can calculate the moles of Na₂O
moles of MgCl₂ = 1/1 x moles of MgO
Moles of MgCl₂ = 1.3148 moles
Then calculate the mass of Na₂O
MgCl₂ molar mass is equal to its molecular weight times moles
mass MgCl₂ = 1.3148 moles* 95.211 g/mol. = 125.18 g
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How do the ideas of electrolytes and IV fluids relate?
Answer:
Electrolytes, particularly sodium, help the body maintain normal fluid levels in the fluid compartments because the amount of fluid a compartment contains depends on the amount (concentration) of electrolytes in it. If the electrolyte concentration is high, fluid moves into that compartment (a process called osmosis).
Explanation:
Answer:
Electrolytes are minerals in your body that have an electric charge. They are in your blood, urine, tissues, and other body fluids. Electrolytes are important because they help
Balance the amount of water in your body
Balance your body's acid/base (pH) level
Move nutrients into your cells
Move wastes out of your cells
Make sure that your nerves, muscles, the heart, and the brain work the way they should
Sodium, calcium, potassium, chloride, phosphate, and magnesium are all electrolytes. You get them from the foods you eat and the fluids you drink.
The levels of electrolytes in your body can become too low or too high. This can happen when the amount of water in your body changes. The amount of water that you take in should equal the amount you lose. If something upsets this balance, you may have too little water (dehydration) or too much water (overhydration). Some medicines, vomiting, diarrhea, sweating, and liver or kidney problems can all upset your water balance.
Treatment helps you to manage the imbalance. It also involves identifying and treating what caused the imbalance.
hope it's help you plz mark as brain listclassify the substances according to the strongest solute-solvent interaction that will occur between the given substances and water during dissolution.
Intermolecular interaction occurs between the given substances and water during dissolution according to the strongest solute-solvent interaction.
Intermolecular bonds in covalent substances are Hydrogen bond. Dipole-dipole attraction, Dipole-induced dipole attraction , London dispersion forces. Water has polar OH bond. The negative O atom attract the positive H atoms in nearby molecules. It leads to the Hydrogen bonds. It is also called Dipole-dipole Force. Dipole -dipole forces occur between the water and substance during dissolution according to the strongest solute-solvent interaction. Hydrogen bonds are the strongest force present in the water dissolution. London dispersion force is also present in the water dissolution.
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Is the movement of breakdown products of food from the lumen of the small intestine into the blood or lymph?
Absorption is the movement of breakdown products of food from the lumen of the small intestine into the blood or lymph.
The digestive system breaks down the food into their smaller components. The digestive system consists of the stomach, intestines, liver, pancreas, mouth, esophagus, etc. After food is broken down into smaller monomers, it is absorbed by blood and lymph. This process is called absorption. Most of the absorption occurs through the linings of the small intestines, but some of it occurs in the mouth (starch is absorbed here), the stomach (alcohol, some fats and proteins are absorbed here), and the large intestine (water, vitamins, and minerals). Thus, absorption is correct answer for this question.
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Complete question:
____Is the movement of breakdown products of food from the lumen of the small intestine into the blood or lymph?
a. Propulsion
b. Ingestion
c. Chemical digestion
d. Defecation
e. Absorption
What is the difference between intermolecular forces of attraction and covalent bonds and how do I know if its strong or weak
Answer:
An intermolecular force is the force of attraction or repulsion which act between neighboring particles (atoms, molecules, or ions). Whereas the covalent bonds are the interatomic linkage that results from the sharing of an electron pair between two atoms.
Intermolecular forces hold molecules together in a liquid or solid. Intermolecular forces are generally much weaker than covalent bonds.
When Alyssa did Part A of the experiment, she observed the solutionoutside the tubing turn black. What might have happened?
The solution outside the tubing might have reacted with the air, causing oxidation and turning black.
When Alyssa performed Part A of the experiment, she observed that the solution outside the tubing turned black. This could be due to a process known as oxidation.
Oxidation is a chemical reaction that occurs when a substance reacts with oxygen in the air. The reaction causes the substance to lose electrons, which can cause a change in color, among other things.
In this case, the solution outside the tubing may have reacted with oxygen in the air, causing it to turn black. This reaction could have been facilitated by heat, light, or other factors that can increase the rate of oxidation. Additionally, the composition of the solution and the presence of any catalysts could have also contributed to the reaction.
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(EASY POINTS!!!!!!!!!!!!!!!)How do we change the world... one random act of kindness at a time
Answer:
less polution
Explanation:
what is the formal concentration (expressed as mol/l = m) of nacl when 32.0 g are dissolved in water and diluted to 0.500 l
When 32.0 g of NaCl are dissolved in water and diluted to 0.500 L, 1.10 M of NaCl is the formal concentration (expressed as mol/L or M).
To find the formal concentration, we need to determine the number of moles of NaCl present in the solution. The molar mass of NaCl is 58.44 g/mol, so to find the number of moles, we divide the mass of NaCl by its molar mass:
Number of moles = Mass / Molar mass of sodium chloride (NaCl)
Number of moles = 32.0 g / 58.44 g/mol = 0.548 mol
Next, we need to calculate the formal concentration by dividing the number of moles by the volume of the solution in liters:
Formal concentration = Number of moles / Volume of solution
Formal concentration = 0.548 mol / 0.500 L = 1.10 M.
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The absorption spectrum of a molecular compound in the microwave radiation range provides information about the: 1.Electronic structure of the molecule 2. Bonds and bond energies of the molecule 3. Shape of the molecule
Answer: 2. Bonds and bond energies of the molecule
Explanation:
The absorption spectrum is an electromagnetic spectrum which is used for observing the intensity of the radiations which have been absorbed by the substances shown by the pattern of dark lines or bands. Infrared and microwave spectroscopy are specialized techniques which are used for observing the bonds and bond energy of the molecules which can be observed by measuring the frequencies at which the radiations are absorbed.
Identifying Characteristics of Atoms
Number of
Protons
Number of
Neutrons
Atomic
Number
Mass
Number
Element
(symbol)
А
7
B
15
С
D
E
26
56
F
Using the periodic table, complete the table to describe each atom. Type in your answers,
А
00
С
F
Explanation:
The number of protons in an atom is the atomic number.
Mass number is the number of protons plus neutrons in an atom.
Mass number = number of protons + number of neutrons
Atomic number = number of protons
Atomic number gives the symbol of the element
Number Number Atomic Mass Symbol
Protons neutrons Number Number
A 7 B 15 C
D E 26 56 F
A, number of protons = B
Mass number = protons + neutrons
15 = protons + 7
Protons = 15 - 7 = 8
Atomic number 8 is for oxygen = C
Atomic number = number of protons = D = 26
Number of neutrons ;
E = Neutrons = mass number - protons = 56 - 26 = 30
Atomic number 26 is for Iron = F
Why is making proteins important
If three molecules of hydrogen react with one molecule of nitrogen, how many molecules of ammonia would be formed?
1
2
3
4
Answer:
The answer to your question is 2 molecules, or B(edg 2021).
Explanation:
edg 2021
A woman uses 330 Joules of energy to push a box across the floor in 33 seconds. What is her power output in Watts?
Answer:
10 watts
Explanation:
Power = Work / Time
Power = 330 J / 33 s
Power = 10 watts
Which of the following is an example of a heterogeneous mixture?
salad
milk
paint
toothpaste
Answer:
salad
Explanation:
1.
7.5A In what form do plants store the energy produced from sunlight?
Answer:
photosynthesis
Explanation:
Bc it is
The moles is a counting unit defined as 1 mole = 6.022 × 10^23 objects. If you have a sample with 3.41 × 10^24 H2O molecules, how many moles of hydrogen atoms would the sample contain?Enter the value using exponential notation, e.g. 1.23 × 10^4 would be entered as 1.23E4.(value ± 2%)
The number of moles of the hydrogen atoms that would the sample of the H₂O contain is 1.04 E¹.
1 mole of substance = 6.022 × 10²³ molecules
The molecules of water = 3.41 × 10²⁴ molecules of the water
18 g of water = 1 mole = 3.41 × 10²⁴ molecules of water
1.008 g of hydrogen = 1 mole = 3.41 × 10²⁴ atoms of hydrogen
The moles of H atom = (2 × 3.41 × 10²⁴ ) 6.022 × 10²³ molecules of H₂
The moles of the H atom = 1.04 × 10¹ moles
Thus, the value using exponential notation is 1.04 E¹.
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Directions: Convert the following word equations into formula equations then balance
them.
1. zinc + nitrogen → zinc nitride
..............
......
The word equations into formula equations can be written as .\(3Zn+N_{2}\to Zn_{3}N_{2}\)
What is a formula equation?The formula is a fact or a rule written with mathematical symbols.
It is the symbolic representation of a chemical equation.
Symbol for zinc is Zn and that for nitrogen gas is N₂.
In general, \(Zn+N_{2}\to Zn_{3}N_{2}\) is the formula equation of
zinc + nitrogen → zinc nitride.
Now, the balanced chemical equation for the given condition can be written as,
\(3Zn+N_{2}\to Zn_{3}N_{2}\)
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how many moles of NH, will be produced if 3.5 moles of N2, are reacted completely
If 3.5 moles of N2 are reacted completely, 7 moles of NH3 will be produced.
To determine the number of moles of NH3 produced when 3.5 moles of N2 are reacted completely, we need to examine the balanced chemical equation for the reaction.
The balanced equation for the reaction between N2 and H2 to form NH3 is:
N2 + 3H2 → 2NH3
From the balanced equation, we can see that 1 mole of N2 reacts to form 2 moles of NH3.
Given that we have 3.5 moles of N2, we can use the stoichiometry of the reaction to calculate the moles of NH3 produced.
Using a ratio, we can set up the following proportion:
(3.5 moles N2) / (1 mole N2) = (x moles NH3) / (2 moles NH3)
Cross-multiplying and solving for x (moles NH3):
x = (3.5 moles N2 * 2 moles NH3) / (1 mole N2)
x = 7 moles NH3
It's important to note that this calculation assumes the reaction goes to completion, meaning all reactants are completely consumed to form the products according to the stoichiometry of the balanced equation. In actual reactions, there may be limiting reactants or other factors that affect the yield of the product.
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1. Isotopes of are atoms of the same element that vary in
A. protons
B. neutrons
C. protons and neutrons
D. neutrons and mass
2. What do these 2 atoms have in common? B-10 and B-11?
A. both have same number of neutrons
B. both have 5 electrons
C. both have 6 protons
D. both have same mass
Explain how you got your answer
Answer:
1. D
2. B
Explanation:
1. Isotopes vary in neutrons. Due to this variance, the difference in neutrons change the mass of the element.
Note: the amount of protons in an element never changes. The number of protons (the atomic number on the periodic table) identifies the element in question. If you add or subtract protons, you change the element.
2. B-10 and B-11 are two isotopes of the element Boron: One with 10 neutrons, and another with 11 neutrons. Because they contain a variance of neutrons, they do not have the same mass. This cancels choices A and D.
The protons of an element are equal to the atomic number of that element. Borons atomic number is 5 (according to the periodic table), so it contains 5 protons. This cancels choice C as the element with 6 protons is Carbon.
Note: The amount of protons in an atom is balanced out by the same amount of electrons to allow for a neutral charge of the element (i.e., the protons, which contain a positive charge, and electrons, which contain a negative charge, cancel each other out. In the case of Boron: +5 protons - 5 electrons = 0 charge). This is why choice B is correct, as the consideration of an ion is not necessary for this question.
The disinfectant hydrogen peroxide (H2O2)
decomposes to form water and oxygen gas.
How much O2 will result from the decomposition of 2.22 mol of hydrogen peroxide?
Answer:
1.1 mol of O2
Explanation:
First we need the balance chemical equation which is
2 H2O2 -------> 2 H2O + O2
This is important because in stoichiometry you can go from units of one thing to other by using mole ratios, here the mole ratio is 2 mol of H2O2 for one mole of O2.
\(2.2 mol H2O2 \frac{1mol O2}{2 mol H2O2}\) = 1.1 mol of O2
For the combustion of propane (c3h8), how many grams of oxygen are needed to fully react 45.0 grams of propane? report your answer to the nearest whole number.
For the combustion of propane \(C_{3}H_{8}\), 164 grams of oxygen is needed to fully react 45.0 grams of propane.
We know that,
The combustion of propane is as follows:-
\(C_{3}H_{8}+5O_{2}\) → \(3CO_{2}+4H_{2}O\)
Hence, for 1 mole of propane 5 moles of \(O_{2}\) are needed.
We know that,
Mass of 1 mole of propane = 12*3 + 1*8 = 36+8 = 44g
Hence,
45g of propane = 45/44 moles of propane = 1.022 moles.
Hence,
1.022 moles of propane will need 5*1.022 = 5.11 moles of \(O_{2}\).
1 mole of \(O_{2}\) = 2*16 = 32g
5.11 moles of \(O_{2}\) = 32*5.11 = 163.52g ≈ 164g \(C_{3}H_{8}\), 164 grams of oxygen are needed to fully react 45.0 grams of propane.
We know that,
The combustion of propane is as follows:-
\(C_{3}H_{8}+5O_{2}\) → \(3CO_{2}+4H_{2}O\)
Hence, for 1 mole of propane 5 moles of \(O_{2}\) are needed.
We know that,
Mass of 1 mole of propane = 12*3 + 1*8 = 36+8 = 44g
Hence,
45g of propane = 45/44 moles of propane = 1.022 moles.
Hence,
1.022 moles of propane will need 5*1.022 = 5.11 moles of \(O_{2}\).
1 mole of \(O_{2}\) = 2*16 = 32g
5.11 moles of \(O_{2}\) = 32*5.11 = 163.52g ≈ 164 grams.
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What is the wavelength (in nm) of an electron with the following kinetic energies? (a) 20.0 ev (no response) nm (b) 200 ev (no response) nm (c) 2.00 kev (no response) nm (d) 20.0 kev (no response) nm (e) 0.200 mev (no response) nm (f) 2.00 mev (no response) nm which of these energies are most suited for study of the nacl crystal structure? (select all that apply.) 20.0 ev 200 ev 2.00 kev 20.0 kev 0.200 mev 2.00 mev none of these
The wavelength of an electron can be calculated using the formula: wavelength = h / (mass of electron * velocity). Since kinetic energy is equal to the mass of the electron multiplied by the velocity squared, we can also calculate wavelength by using the formula: wavelength = h / sqrt(2mass of electron kinetic energy).
To convert the kinetic energies given in electron volts (eV) to Joules (J), you can use the formula: 1 eV = 1.6 x 10^-19 J
(a) 20.0 eV = 3.2 x 10^-18 J, wavelength = h / sqrt(2mass of electron3.2 x 10^-18 J) = 2.4 x 10^-12 m or 2.4 pm (picometers)
(b) 200 eV = 3.2 x 10^-17 J, wavelength = h / sqrt(2mass of electron3.2 x 10^-17 J) = 2.4 x 10^-11 m or 24 pm
(c) 2.00 keV = 3.2 x 10^-14 J, wavelength = h / sqrt(2mass of electron3.2 x 10^-14 J) = 2.4 x 10^-8 m or 2.4 nm
(d) 20.0 keV = 3.2 x 10^-13 J, wavelength = h / sqrt(2mass of electron3.2 x 10^-13 J) = 2.4 x 10^-7 m or 24 nm
(e) 0.200 MeV = 3.2 x 10^-11 J, wavelength = h / sqrt(2mass of electron3.2 x 10^-11 J) = 2.4 x 10^-5 m or 0.24 nm
(f) 2.00 MeV = 3.2 x 10^-10 J, wavelength = h / sqrt(2mass of electron3.2 x 10^-10 J) = 2.4 x 10^-4 m or 2.4 nm
A lower energy electron will have a longer wavelength, while a higher energy electron will have a shorter wavelength. To study the crystal structure of NaCl, you would need to use a technique such as X-ray diffraction, which typically uses X-rays with energies in the range of a few keV to a few tens of keV. Based on this, 2.00 keV and 20.0 keV energies are most suited for study of the NaCl crystal structure.
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Why does less evaporation mean higher temperatures in urban areas?
Less evaporation means that less of the sun's energy is used to convert water into water vapor, and more of it is used to heat up the surface. In urban areas, there is typically less vegetation and more impervious surfaces (such as concrete and asphalt), which reduces the amount of water that can evaporate.
This means that more of the sun's energy is absorbed by the surface, leading to higher temperatures. Additionally, buildings and other structures in urban areas can trap heat and prevent it from dissipating, further contributing to the urban heat island effect.
In rural areas, vegetation and soil moisture play an important role in regulating temperature through a process called evapotranspiration. Evapotranspiration is the combined process of water evaporation from the soil and plant transpiration. It helps to cool the air by removing heat from the surface through the transfer of water from the surface to the atmosphere.
In contrast, urban areas have a significant amount of impervious surfaces like concrete, asphalt, and buildings, which reduce the amount of vegetation and soil moisture. As a result, urban areas have less evapotranspiration, which means less cooling effect from the evaporation of water. This leads to a higher surface temperature in urban areas.
Furthermore, urban areas have a higher proportion of dark-colored surfaces, such as asphalt and concrete, which absorb more solar radiation than lighter-colored surfaces like vegetation and soil. This is known as the "urban heat island effect," which further contributes to higher temperatures in urban areas.
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Question 7
Review
The solubility of KCl(s) in water depends on the
a
pressure on the solution
b.
rate of stirring
size of the KCl sample
d
temperature of the water
Submit Answer
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To separate a mixture of large gravel and sand, the most effective method would be
Answer:
Sieve
Explanation:
A sieve or screen would be the best tool to use when separating a mixture of sand and gravel.
Answer:
the third option on edge:)
Explanation:
. At time t=0, an aluminum bar (thermal diffusivity k=0.86 ) of length Lcm with completely insulated lateral surfaces and constant thermal properties is removed from boiling water (uB=100 degrees Celsius). Do the following i), ii), iii) for each of the scenarios, a-d, below i) Write down the initial-boundary value problem. That is, the PDE along with any initial and boundary conditions. ii) Without solving for u(x,t), describe the temperature distribution in the bar as t→[infinity] based on physical intuition. iii) Find the solution as t→[infinity] by solving the appropriate steady state equation. a) The two ends of the bar are immediately immersed in a medium with constant temperature 10 degrees Celsius. b) The end at x=0 is immersed in a medium with temperature 0 degrees Celsius and the end at x=L is completely insulated.
(i) The initial-boundary value problem for the given scenarios are as follows:
a) Scenario a:
PDE: ∂u/∂t = k * ∂²u/∂x²
Initial condition: u(x, 0) = 100 (boiling water temperature)
Boundary conditions: u(0, t) = 10, u(L, t) = 10 (constant temperature at the ends)
b) Scenario b:
PDE: ∂u/∂t = k * ∂²u/∂x²
Initial condition: u(x, 0) = 100 (boiling water temperature)
Boundary conditions: u(0, t) = 0 (temperature at x=0), ∂u/∂x(L, t) = 0 (thermal insulation at x=L)
(iii) The solution for the temperature distribution as time approaches infinity can be found by solving the appropriate steady state equation.
What is the expected temperature distribution in the bar as time approaches infinity?(i) The initial-boundary value problem formulation states the partial differential equation (PDE) governing the temperature distribution in the aluminum bar, along with the initial condition and boundary conditions.
In scenario (a), both ends of the bar are immersed in a medium with a constant temperature of 10 degrees Celsius, while in scenario (b), the end at x=0 is immersed in a medium with temperature 0 degrees Celsius and the end at x=L is insulated.
(ii) As time approaches infinity, the temperature distribution in the bar tends to reach a steady state.
In scenario (a), the temperature throughout the bar will eventually approach a constant value of 10 degrees Celsius, since both ends are immersed in a medium with that temperature.
In scenario (b), the temperature at x=0 will approach 0 degrees Celsius, while the temperature at x=L will remain constant due to thermal insulation.
(iii) To find the solution as time approaches infinity, we need to solve the appropriate steady state equation.
In scenario (a), the steady state equation is ∂²u/∂x² = 0, which implies that the temperature gradient is zero throughout the bar, resulting in a constant temperature of 10 degrees Celsius.
In scenario (b), the steady state equation is ∂²u/∂x² = 0 with the boundary condition u(0) = 0, which implies a linear temperature distribution from 0 degrees Celsius at x=0 to a constant temperature at x=L due to insulation.
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Explain why this compound is not a hydrocarbon. *
(2 points)