Name: golden gate bridge thermal expansion
Uploaded: 2023-09-18T17:11:17.000Z
Duration: 1 min 27 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.13

CHEM.13.D

thermal-expansion-and-thermal-stress-problem-solving

Thermal expansion and Thermal stress: Problem Solving

Металлическая проволока длиной 75 сантиметров помещается внутрь печи при температуре 450 градусов Цельсия. Если длина провода меняется на 75,77 сантиметра, а температура в помещении составляет 20 градусов по Цельсию, оцените коэффициент линейного расширения материала провода.
После охлаждения оба конца проволоки крепятся к подставке и помещаются внутрь печи при температуре 200 градусов Цельсия. Оцените создаваемое тепловое напряжение, если модуль Юнга составляет 7,0 x10 10 Паскалей, и определите материал провода.
Коэффициент линейного расширения провода зависит от начальной длины, температурного градиента и изменения длины и рассчитывается как 2,4 х 10-5 градусов Цельсия.
Кроме того, создаваемое тепловое напряжение может быть рассчитано с использованием модуля Юнга, температурного градиента и коэффициента линейного расширения материала провода и рассчитывается как 3,02 x 102 мегапаскалей.
Значения коэффициента расширения и модуля Юнга позволяют предположить, что проволока, скорее всего, изготовлена из алюминия.

<ol>
	<li>OpenStax. (2019). Университетская физика Том 2. [Веб-версия]. Получено из <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; С. 15, 18.</li>
</ol>

Термическое расширение и термическое напряжение: решение задачи

Золотой мост Голден Гейт в Сан-Франциско подвержен температурам от -15 °C до 40 °C. В самый холодный момент основной пролёт моста имеет длину 1275 метров. Предполагая, что мост полностью состоит из стали, каково изменение его длины при таких температурах?

Чтобы решить проблему, в первую очередь определите известные и неизвестные величины. Начальная длина (L) моста составляет 1275 метров, коэффициент линейного расширения (α) для стали равен 12 x 10-6/°C, а изменение температуры (ΔT) составляет 55 °C.

Напомним, что термическое расширение - это расширение материала с увеличением температуры. Линейное расширение - это изменение длины вещества при изменении температуры, и оно пропорционально начальной длине и изменению температуры. Постоянная пропорциональности - это коэффициент линейного расширения. Используя уравнение для линейного термического расширения для расчета изменения длины, ΔL:

<img alt="Equation1" src="/files/ftp_upload/14164/14164_equation_2v2.svg" style="text-align: center; height: 16px;" />

Подставляя все известные значения в уравнение, чтобы найти изменение длины, ΔL:

<img alt="Equation2" src="/files/ftp_upload/14164/14164_equation_2.svg" style="text-align: center; height: 20px;" />

Изменение длины Золотого моста составляет 0,84 метра. Хотя это изменение длины небольшое по сравнению с длиной моста, оно заметно. Как правило, оно распределяется на множество стыков расширения, чтобы расширение на каждом стыке было незначительным.

Кроме того, если изменить температуру объекта, предотвратив его расширение или сжатие, объект подвергается термическому напряжению. Чтобы рассчитать термическое напряжение в объекте, где оба конца жёстко закреплены, напряжение можно рассматривать как развивающееся в два этапа. Сначала позвольте концам свободно расшириться или сжаться и найдите расширение или сжатие. Затем найдите напряжение, необходимое для сжатия или растяжения объекта до его исходной длины с помощью методов, изученных в статическом равновесии и упругости. Другими словами, изменение длины от термического расширения равно изменению длины от упругой деформации, за исключением противоположных знаков.

Мост Золотые Ворота в Сан-Франциско подвергается воздействию температур от -15 °C до 40 °C. В самый холодный период главный пролет моста ...

Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Temperature and Heat

Температура и тепло

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

golden gate bridge thermal expansion

Thermal expansion and thermal stress are shown through the Golden Gate Bridge. The bridge faces temperatures from -15 °C to 40 °C. At its coldest, the main span is 1275 m long. Assuming the bridge is made entirely of steel, the example asks for the change in its length across this temperature range.

To solve the problem, the known values must be identified first. The initial length is 1275 m. The coefficient of linear expansion for steel is 12 x 10 -6 /°C, and the change in temperature is 55 °C. Linear expansion means a material changes length when temperature changes, and the change is proportional to the original length and the temperature change.

The calculation uses the equation for linear thermal expansion to find ΔL. After substituting the given values, the change in length is 0.84 m. That change is small compared with the full span, but it is still observable. In practice, it is spread over many expansion joints so the expansion at each joint stays small.

The same situation also helps explain thermal stress. If an object is heated or cooled while both ends are held rigidly, it cannot expand or contract freely. The stress can be found in two steps. First, let the object expand or contract freely and find ΔL. Then find the stress needed to bring it back to its original length. The thermal expansion ΔL and the elastic distortion ΔL are equal in size, but their signs are opposite.

Golden Gate Bridge Thermal Expansion

temperature and thermal equilibrium

Heat, Temperature, and Everyday Energy

Heat and temperature are key ideas in thermodynamics and in everyday life. People often connect temperature with hot and cold, but science gives it a more precise meaning. Temperature is the quantity measured with a thermometer. It is also linked to the average translational kinetic energy of particles. Heat is different from temperature. Heat is energy that moves from one place or material to another because there is a difference in temperature. That difference in temperature keeps heat...

zeroth law of thermodynamics

Thermal Equilibrium and the Zeroth Law

The zeroth law of thermodynamics explains thermal equilibrium between objects. If object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is also in equilibrium with object C. This transitive relationship is the key idea behind the law. A simple example uses metal blocks and a metal plate at room temperature. A cold metal block and a hot metal block are both placed on the plate. Over time, the cold block and the plate reach thermal equilibrium, and...

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How Thermometers Measure Heat

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gas thermometers and the kelvin scale

Kelvin Temperature and Gas Thermometer Standards

Kelvin temperature is the absolute scale used in science, and it starts at absolute zero. That zero point matches the lowest possible temperature, where molecular motion reaches zero or the minimum allowed by quantum mechanics. Scientists use this scale because some physical quantities, such as the volume of an ideal gas, depend directly on absolute temperature. The Kelvin scale is part of the SI system of units, so its definition is more precise than simply using water’s freezing and boiling...

thermal expansion

Thermal Expansion in Air, Water, and Solids

Thermal expansion is the change in size or volume of a material as its temperature changes. A common example is the alcohol inside a thermometer. As the temperature rises, the alcohol expands and shows the change. Heated air also expands. It becomes less dense than the cooler air around it, so the surrounding air pushes it upward. This is why steam and smoke rise and why hot air balloons float. The same effect happens in liquids and gases, and it helps move heat upward in homes, oceans, and...

thermal stress

How Temperature Changes Create Stress

Thermal stress is the stress that builds up when an object changes temperature but cannot expand or contract freely. If the object would expand without restraint, the stress is compressive. If it would contract, the stress is tensile. This stress from heating or cooling can become large enough to cause damage. Engineers often reduce it by designing parts so they can move as temperature changes. Highway blocks, for example, are separated by gaps so thermal stress does not build up. When gaps...

thermal expansion and thermal stress: problem solving

Thermal expansion and thermal stress are shown through the Golden Gate Bridge. The bridge faces temperatures from -15 °C to 40 °C. At its coldest, the main span is 1275 m long. Assuming the bridge is made entirely of steel, the example asks for the change in its length across this temperature range. To solve the problem, the known values must be identified first. The initial length is 1275 m. The coefficient of linear expansion for steel is 12 x 10 -6 /°C, and the change in temperature is 55...

heat flow and specific heat

Heat Units and Specific Heat

Heat is energy transferred because of a temperature difference, and it can change an object’s temperature. Since heat is energy, its SI unit is the joule (J). Heat transfer is the movement of energy from one place or material to another, and it plays a role in home heating, cooking, and many industrial processes. Two common units for heat are the calorie and the kilocalorie. A calorie (cal) is the energy needed to change the temperature of 1 g of water by 1 °C, specifically between 14.5 °C and...

phase changes

Heat and Phase Change Energy

Heat and phase change energy explain why substances melt, freeze, boil, and condense. A solid turns into a liquid during melting, also called fusion. The reverse process is freezing. A liquid turns into a gas during evaporation. The reverse process is condensation. Each substance changes phase at specific temperatures. The melting point is the temperature where a substance melts or freezes. The boiling point is the temperature where a substance boils or condenses. These temperatures depend on...

calorimetry

Heat Exchange in an Insulated System

Calorimetry studies heat exchange in an insulated system. A calorimeter is a container that prevents heat transfer in or out. Scientists use calorimetry to measure heat and specific heat capacity. A calorimetry problem is any situation where the objects are thermally isolated from their surroundings. The key idea comes from conservation of energy. During heat transfer, the heat gained by the colder object must equal the heat lost by the hotter object. A simple example is water poured into a...

mechanisms of heat transfer i

Three Ways Heat Moves Between Objects

Heat transfer happens when there is a temperature difference. It can move fast, like through a cooking pan, or slowly, like through the walls of a picnic ice box. Heat transfer appears in many everyday situations, so it is hard to find a place where it does not occur. There are only three ways heat is transferred: conduction, convection, and radiation. A fireplace shows all three at once. Radiation carries most of the heat into the room. Conduction also moves heat into the room, but much more...

mechanisms of heat transfer ii

Convection and Radiation in Heat Transfer

Convection and radiation are two major ways heat moves. In convection, thermal energy is carried by the large-scale flow of matter. Warm air and water rise because they are less dense, so ocean currents and large-scale atmospheric circulation move heat from the tropics toward the poles and move cold air from the poles toward the tropics. Earth’s rotation changes these moving air currents. It interacts with the flow and helps produce the eastward movement of air in the temperate zones.

conduction, convection and radiation: problem solving

conduction-convection-and-radiation-problem-solving

Heat Transfer Calculations with Conduction, Convection

Heat transfer calculations with conduction and convection use the temperature difference to find the rate of heat flow. Radiation can also be part of the process. The main idea is that heat moves only because one area is hotter than another, and a larger temperature difference leads to faster transfer. To solve a heat transfer problem, first identify the type of transfer involved. It may be conduction, convection, radiation, or a combination of all three. Next, write down the unknown...

radiation: applications

Earth’s Energy Balance and Greenhouse Effect

Earth’s energy balance and the greenhouse effect help explain its average temperature. Earth is in radiative contact with both the Sun and dark space. It receives almost all of its energy from solar radiation, and it reflects some of that energy back into outer space. Dark space is very cold, about 3 K, so Earth also radiates energy into it. Heat can move quickly from soil and grasses, and frost can form on clear summer evenings, even in warm latitudes. In a first approximation, Earth’s...

absorption of radiation

Radiation Heat Transfer and Thermographs

Radiation heat transfer depends on temperature, surface area, and emissivity. The Stefan-Boltzmann law describes the rate of heat transfer by emitted radiation. In this law, σ is the Stefan-Boltzmann constant, A is the object’s surface area, and T is its temperature in kelvins. The fourth-power dependence on absolute temperature makes radiation highly sensitive to small temperature changes. Even a slight rise in temperature can change the emitted heat a lot. That sensitivity is why radiation...

key terms and concepts

Use the Golden Gate Bridge to calculate linear thermal expansion, find the 0.84 m length change, and see how fixed ends create thermal stress.

Golden Gate Bridge Thermal Expansion | JoVE K12

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JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

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CHEM.13.A

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CHEM.13.B

CHEM.13.C

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San Francisco&#39;s Golden Gate Bridge is exposed to temperatures ranging from -15 &#176;C to 40 &#176;C. At its coldest, the main span of the bridge is ...

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The specific heat capacity of a substance refers to the energy required to increase the temperature of one gram of that substance by one degree Celcius. ...

Science concepts. The student understands the energy changes that occur in chemical reactions. The student is expected to:

Golden Gate Bridge Thermal Expansion

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