Materials expand when heated. Consider a metal rod of length L0 at temperature T0. If the temperature is changed by an amount ΔT, then the rod’s length changes by ΔL=αL0ΔT, where α is the thermal expansion coefficient.
For steel, α=1.24×10−5∘C−1.(a) A steel rod has length L0=40cm at T0=40∘C. What is its length at T=180∘C?
(Use decimal notation. Give your answer to three decimal places.)
L≈cm
(b) Find its length at T=90∘C if its length at T0=120∘C is 65 in.
(Use decimal notation. Give your answer to three decimal places.)
L≈ in.
(c) Express length L as a function of T and α if L0=60in. at T0=150∘C.
(Use symbolic notation and fractions where needed.) L(T,α)=

Answers

Answer 1

Answer:

(a) The length at temperature 180°C is 40.070 cm

(b) The length at temperature 90°C is 64.976 inches

(c) L(T, α) = 60·α·T - 9000·α + 60

Explanation:

(a) The given parameters are

The thermal expansion coefficient, α for steel = 1.24 × 10⁻⁵/°C

The initial length of the steel L₀ = 40 cm

The initial temperature, t₀ = 40°C

The length at temperature 180°C = L

Therefore, from the given relation, for change in length, ΔL, we have;

ΔL = α × L₀ × ΔT

The amount the temperature changed ΔT = 180°C - 40°C = 140°C

Therefore, the change in length, ΔL, is found as follows;

ΔL = α × L₀ × ΔT = 1.24 × 10⁻⁵/°C × 40 × 140°C = 0.07 cm

Therefore, L =  L₀ + ΔL = 40 + 0.07 = 40.07 cm

The length at temperature 180°C = 40.07 cm

(b) Given that the length at T = 120°C is 65 in., we have;

The temperature at which the new length is sought = 90°C

The amount the temperature changed ΔT = 90°C - 120°C = -30°C

ΔL = α × L₀ × ΔT = 1.24 × 10⁻⁵/°C × 65 × -30°C = -0.024375 inches

The length, L at 90°C is therefore, L = L₀ + ΔL = 65 - 0.024375 = 64.976 in.

The length at temperature 90°C = 64.976 inches

(c) L = L₀ + ΔL  = L₀ +  α × L₀ × ΔT = L₀ +  α × L₀ × (T - T₀)

Therefore;

L = 60 +  α × 60 × (T - 150°C)

L = 60 + α × 60 × T - 9000 × α

L(T, α) = 60·α·T - 9000·α + 60


Related Questions

ASAP!
A solution is made by dissolving 125 g of sodium chloride in 1.5 kg of water. What is the percent by mass?​

Answers

Answer:

8.3334%

Explanation:

You have two masses. To find the percent of sodium chloride in water by mass, you divide the mass of NaCl by water. First, make both units the same. Easiest is to convert kg into g. 1.5kg = 1500g

125g NaCl/1500g H2O = 0.0833333333 ==> 8.3334%

Which statement accurately compares the trends in atomic number and atomic mass in the periodic table

Answers

the  Answer is C

Both the atomic mass and the atomic number increase from left to right.

Answer: is C

Explanation:

Both the atomic mass and the atomic number increase from left to right

she adds 1.5 mL, 0.75 mL, and 1.2 mL. Her measurements of the oil are blank

Answers

Answer:

The total measurements of the oil is 3.45mL

Explanation:

Given

1.5 mL, 0.75 mL, and 1.2 mL.

Required

Determine the total

To get the total, we simply add the given volumes together.

[tex]Total = 1.5 mL+ 0.75 mL + 1.2 mL[/tex]

[tex]Total = 3.45mL[/tex]

Hence;

The total measurements of the oil is 3.45mL

A single atom of an element has 11 protons, 11 electrons, and 12 neutrons. Which element is it? a V b Na c Mg d Se

Answers

Answer:

B.  Na

Explanation:

To identify an atom, you simply need to look at the number of protons.  This atom has 11 protons.  On the periodic table, you can see that the element with 11 protons is sodium (Na).

Why do scientists prefer using the Kelvin Scale of temprature?

Answers

Probably because they think it is more accurate.

Hope it helps.

They believe it’s more accurate.

Which statement best compares and contrasts two physical properties of matter?

Answers

Answer:

Answer would be that boiling points and melting points are similar because they both involve the change in a state of a material, but they are different because boiling point involves a change from a liquid to a gas and melting point involves a change from a solid to a liquid. Boiling and melting are phase changes that can happen to a substance however they differ in the process that happens.

Explanation:

Two physical properties of matter can be best compared as boiling points and melting points are similar because both involve the change in a state of matter. But they are different because melting point involves a change from a solid to a liquid and boiling point involves a change from a liquid to a gas.

What are the boiling point and melting point?

A boiling point of a liquid can be described as the temperature at which the vapour pressure is equal to the atmospheric pressure of the liquid. The liquid is changed into a vapour at this temperature.

With the addition of heat, the liquid will change into vapour without any increase in temperature. The vapour pressure of the gas increases until it is equal to the pressure of the gas surrounding it. Bubbles are formed within the liquid and rise to the surface.

The melting point of a substance can be described as the temperature at which it transforms the state from solid to liquid. At the melting point, the solid phases and liquid phases exist in equilibrium. The melting point depends on pressure and is generally specified at a standard pressure such as 1 atmosphere.

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Your question is incomplete, but most probably complete question was,

Which statement best compares and contrasts two physical properties of matter?

A) Density and solubility are similar because they both involve water, but they are different because density involves dissolving a material and solubility involves floating or sinking a material. Density and solubility are similar because they both involve a material’s mass and volume, but they are different because density involves floating materials and solubility involves sinking materials.

B) Boiling points and melting points are similar because they both involve changing the heat of a material, but they are different because boiling point involves adding heat to a material and melting point involves removing heat from a material. Boiling points and melting points are similar because they both involve the change in a state of a material, but they are different because boiling point involves a change from a liquid to a gas and melting point involves a change from a solid to a liquid.

need help asp thank you​

Answers

Answer:

formed at earths surface

Explanation:

so easy

A small rock with the mass of 6 g is dropped into a graduated cylinder with 20 mL of water. The water rises to 23 mL. What is the density of the rock?

Answers

Answer: The density of the rock is 2g/mL. Hope this helped! :)

Explanation:

V= 3.0mL                                                               D=M/V

M= 6.0g

D=6.0g/3.0mL

D= 2.0g/mL

How many significant figures are in 10.060 L?

Answers

Answer:

5

Explanation:

you have two zeros that are sandwiched in between and one following a signifincant figure after the decimal.

Which of the following is a true statement? Smashing an object into many pieces changes its chemical composition. Smashing an object into many pieces is a chemical change. Smashing an object into many pieces does not change the object. Smashing an object into many pieces is a physical change.

Answers

Answer:smashing an object into many pieces is a physical change

Explanation:

becauseee i’m not sure i’m getting points

Answer:

smashing an object into many pieces is a physical change

Explanation:

Fill in the blanks below.
1. The equation shows a _________the breaking and forming of chemical bonds that leads to a change in the composition of matter
2. In the equation, CO2 is a________
3. In the equation, C6H1206 is a ___________
4. In O2, the type of bond that holds the two oxygen atoms together is a___________
5. In H2O, the type of bond that holds one of the hydrogen atoms to the oxygen atom is a________
6. The number of oxygen atoms on the left side of the equation is___________ the number of oxygen atoms on the
Chemical equation
right side.
reactant
product
nonpolar
covalent bond
polar
covalent bond
equal to
different from
hydrogen bond

Answers

Answer:

Explanation:

6CO₂ + 6 H₂O ⇄ C₆H₁₂0₆ + 6O₂

This is the chemical equation given .

1. The equation shows a __Chemical equation_______the breaking and forming of chemical bonds that leads to a change in the composition of matter.

2. In the equation, CO₂ is a___reactant_____.

3. In the equation, C₆H₁₂0₆ is a ___product________.

4. In O₂, the type of bond that holds the two oxygen atoms together is a_nonpolar_covalent bond_________.

5. In H₂O, the type of bond that holds one of the hydrogen atoms to the oxygen atom is a__polar_hydrogen bond____.

6. The number of oxygen atoms on the left side of the equation is__equal to_________ the number of oxygen atoms on the right side.

____is used as anode for prevention of corrosion 1 aluminium 2 magnesium 3 iron

Answers

Answer:

I'm not sure but I think the answer is Cathodic protection.

Question 2

Which statement describes a change of matter that I DIFFERENT from the others?

A

Peroxide breaking down into water and oxygen

B

Bubbles forming when a pot of water is heated

A pair of jeans soaked in water drying after hanging outside

D

A block of ice decreating in size due to a change in temperature

Answers

Answer:

A.  Peroxide breaking down into water and oxygen

Explanation:

Generally when it comes to changes, there are physical and chemical changes. In physical changes, there are no new substances been formed, however in chemical change new substances are formed.

A.  Peroxide breaking down into water and oxygen

This is a chemical change.

B . Bubbles forming when a pot of water is heated

This is a physical change

C. A pair of jeans soaked in water drying after hanging outside

This is a physical change

D . A block of ice decreasing in size due to a change in temperature

This is a physical change.

Only option A is different from the rest,hence this is the answer.

An abandoned Indiana coal mine spoil bank (wastes) contains chunks of pyrite minerals. Under constant erosion and weathering, the pyrites leach large amounts of sulfuric acid (H2SO4). The spoil banks are also mixed with large quantities of basic limestone and clay carbonates. What should occur over time?

Answers

Answer:

The acid will be neutralized overtime

Explanation:

The presence of the pyrites leads to the leaching of large amounts of sulphuric acid, however the basic carbonates neutralizes the acid according to the reaction equation;

CaCO3 + H2SO4 ---> CaSO4 + CO2 + H2O.

This will prevent all the deleterious consequences associated with the leaching of the acid in the abandoned coal mine.

How does scientists benefit society

Answers

Answer:

scientists benefit the society because they prove many theories, plus they are always finding new solutions to new things

Explanation:

Answer:

The scientist uses specialized training to help solve problems

faced by society.

Explanation:

A P E X

The nucleus of a helium atom is identical to: A) a gamma particle B) an alpha particle C) a beta particle D) all of the above

Answers

Answer: D. All of the above

Answer:

B. Alpha Particles

Explanation:

P: Have a Nice Day!

Differences between non-biodegradable and biodegradable.

Answers

Answer:

(simple differences)Biodegradable substances are those that degrades or break down naturally...

Non-biodegradable substances are those that do not degrades easily...

Answer:

Biodegradable substances are those that degrades or break down naturally

Non-biodegradable substances are those that do not degrades easily

Calculate the mass of a liquid with density of 3.20 g/mL and volume of 15.0 mL.

Answers

Answer:

mass = 48 g

Explanation:

The mass of a substance when given the density and volume can be found by using the formula

mass = Density × volume

From the question

Density = 3.20 g/mL

volume = 15.0 mL

Substitute the values into the above formula and solve for the mass

That's

mass = 3.20 × 15

We have the final answer as

mass = 48 g

Hope this helps you

An air mass that originates over land in central america is most likely

Answers

Answer: An air mass that originates over land in Central America is most likely warm & dry.

A liquid that can absorb and release huge amounts of heat energy without much change in the overall temperature of the water has what
A Has a high density capacity
B Has a high surface tension capacity
C Has a high specific leat capacity
D Has a high non-polar capacity

Answers

Answer:

Im pretty sure the answers b

Explanation:

Because if its talking about overall tempature the it means ihas tension with high surface.

If you drop an object with a mass of 3.66 grams and a volume of 4 mL into a beaker containing dish soap, would it float or sink? Dish soap has a density of 0.93 g/mL

Answers

It would most definitely sink

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Answers

Answer:

Explanation:a

Scientific predictions are best described as consistent data that are presented in the form of if and then. It is a solution to the problem that may be identified. Thus, option a is correct.

What is scientific prediction?

Scientific prediction is a statement that describes the events of the future that are not always correct or incorrect. In scientific research, the experiment is conducted based on the hypothesis to draw conclusions and results that are expected.

The expected results are said to be scientific predictions when they are represented in the form of "if and then" before the analysis of the experimental method and its result are done. It is an account of the events that may possibly take place under specific conditions.

Therefore, option A. scientific prediction is an expected problem.

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Put the following elements in order according to the number of protons they contain: S; Si, Sc; Na Reorder answers 1.Si Reorder answers 2.S Reorder answers 3.Sc Reorder answers 4.Na

Answers

Answer:

he oxygen ion you have with 8 protons attracting 10 electrons is larger, ... As a result, the 3Al3+ ion will be smaller than the Si element, which has ... O<Al3+<Si<Al<O2-<Ag<Rb<Cs ... It is fairly easy to arrange the atoms according to atomic size. ... I would put it between Al and Ag .

Explanation:

1. Put 0.000 034 into scientific notation.

Answers

Answer:

3.4x10 to the power of 5

Explanation:

Answer:

My answer to the question is 3.4×10^-5.

How can a new element be made?

Answers

Answer:

adding or removing protons

Explanation:

Elements are defined by the number of protons they have. If you add or subtract protons then that changes and makes a new element.

Answer:

by changing the number of protons in the nucleus

While burning coal and charcoal, you notice that coal releases more heat than charcoal. That means that the... 1. elastic energy 2.gravitational energy 3.chemical potential energy is 1.lower 2. higher in charcoal than in coal

Answers

Answer:

3). Chemical potential energy

1). lower in charcoal than in coal.

Explanation:

Chemical potential energy is defined as the energy that can be absorbed or stored in a substance's chemical bonds. It can be released when there is a change in the number of particles of the substance.

As per the question, coal releases more heat than charcoal because 'the chemical potential energy of charcoal is lower than the coal' and hence, the latter would release more heat on burning i.e. the energy that was absorbed in the chemical bonds of the substance. Hence, option 3 and 1 are the correct answers.

2)
A barbecue is being planned for 175 people. The ice cream sandwiches for desert cost $1.68 per dozen. It is
assumed that the average number of sandwiches eaten per person will be 1.25. What will it cost to buy ice cream
sandwiches for the barbecue. Solve the problem by dimensional analysis.

Answers

Hellppp :( no one is helping me I lost 20 point because no one answer :( plssssss

Dimensional analysis is the unitary method that is used to determine the values by multiplication. The cost of the ice cream sandwiches for the barbecue is 367.5 $.

What is dimensional analysis?

Dimensional analysis has been defined in maths, physics, and chemistry to solve the problem by multiplying the given numbers to determine the values of the other data. It uses the base quantities to estimate the derived values.

Given,

Number of people at barbecue = 175

Cost of ice cream sandwiches = $1.68 per dozen

The average number of sandwiches per person = 1.25

The cost to buy ice cream sandwiches for the barbecue is estimated by the dimensional analysis as:

12 ice cream sandwiches = $1.68

1.25 ice cream sandwiches = $2.1

If it costs $2.1 for each person then 175 people costs:

$2.1 × 175 = $367.5

Therefore, it will cost 367.5 $ for the barbecue.

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why is sodium chloride soluble in water

Answers

Answer: because the very polar water molecules attract both the positively charged sodium ions and the negatively charged chloride ions.

List 3 common examples of physical changes

Answers

crushing a can
breaking glass
boiling water

Answer: crushing a can, boiling water, breaking a glass

Explanation:

what are different type of plastids explain them?​

Answers

Answer:

Explanation:

There are 3 types of plastids :-

1) Chloroplasts:- The green plastids which contain chlorophyll pigments for photosynthesis.

2) Chromoplasts:-The coloured plastids for pigment synthesis and storage.

3) Leucoplasts:- The colourless plastids for monoterpene synthesis found in non- photosynthetic parts of the plants.

They are of three types:-  

a) Amyloplasts- stores starch.

b) Proteinoplasts-  stores proteins.

c) Elaioplasts- stores fats and oils.

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