B)A Thin Spherical Shell Of Silver Has An Inner Radius Of 1.5x102m When The Temperature Is 22oC. The Shell Is Heated To 150oC. The Coefficient Of Volume Expansion Of A Spherical Shell Of Silver Is -1 57x10-6 Oc . What Is The Change In The Interior

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A Thin Spherical Shell of Silver: Understanding the Effects of Temperature Change

In this article, we will explore the effects of temperature change on a thin spherical shell of silver. We will calculate the change in the interior radius of the shell when it is heated from 22°C to 150°C. This problem involves the concept of thermal expansion, which is a fundamental principle in physics.

Thermal Expansion of a Spherical Shell

Thermal expansion is the tendency of matter to change its shape, area, or volume in response to a change in temperature. The coefficient of volume expansion (β) is a measure of the change in volume of a material per unit change in temperature. For a spherical shell, the volume expansion can be calculated using the formula:

ΔV = β * V * ΔT

where ΔV is the change in volume, β is the coefficient of volume expansion, V is the initial volume, and ΔT is the change in temperature.

Calculating the Change in Volume

To calculate the change in volume, we need to know the initial volume of the spherical shell. The volume of a sphere (V) is given by the formula:

V = (4/3) * π * r^3

where r is the radius of the sphere. In this case, the initial radius of the shell is 1.5 x 10^2 m.

First, we need to calculate the initial volume of the shell:

V = (4/3) * π * (1.5 x 10^2 m)^3 = 1.13 x 10^6 m^3

Next, we need to calculate the change in temperature (ΔT):

ΔT = 150°C - 22°C = 128°C

Now, we can calculate the change in volume (ΔV) using the formula:

ΔV = β * V * ΔT = -1.57 x 10^-5 K^-1 * 1.13 x 10^6 m^3 * 128 K = -1.93 x 10^3 m^3

Calculating the Change in Radius

To calculate the change in radius, we need to use the formula:

Δr = ΔV / (4 * π * r^2)

where Δr is the change in radius, ΔV is the change in volume, and r is the initial radius.

First, we need to calculate the initial radius squared:

r^2 = (1.5 x 10^2 m)^2 = 2.25 x 10^4 m^2

Next, we can calculate the change in radius (Δr) using the formula:

Δr = ΔV / (4 * π * r^2) = -1.93 x 10^3 m^3 / (4 * π * 2.25 x 10^4 m^2) = -0.017 m

In this article, we calculated the change in the interior radius of a thin spherical shell of silver when it is heated from 22°C to 150°C. We used the concept of thermal expansion and the coefficient of volume expansion to calculate the change in volume and radius. The results show that the shell will expand by approximately 0.017 m.

  • [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
  • [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

This problem is a classic example of thermal expansion, which is a fundamental principle in physics. The concept of thermal expansion is used to calculate the change in volume and radius of a material when it is heated or cooled. In this case, we used the coefficient of volume expansion to calculate the change in volume and radius of the spherical shell.

The results show that the shell will expand by approximately 0.017 m when it is heated from 22°C to 150°C. This is a significant change in radius, and it highlights the importance of considering thermal expansion in engineering and scientific applications.

  • What is the effect of thermal expansion on the shape of a material?
  • How does the coefficient of volume expansion affect the change in volume of a material?
  • What are some real-world applications of thermal expansion?
  • The effect of thermal expansion on the shape of a material is that it will change its shape, area, or volume in response to a change in temperature.
  • The coefficient of volume expansion affects the change in volume of a material by determining the rate at which the material expands or contracts in response to a change in temperature.
  • Some real-world applications of thermal expansion include the design of buildings, bridges, and other structures that must withstand changes in temperature, as well as the development of materials that can withstand extreme temperatures.
    A Thin Spherical Shell of Silver: Understanding the Effects of Temperature Change - Q&A

In our previous article, we explored the effects of temperature change on a thin spherical shell of silver. We calculated the change in the interior radius of the shell when it is heated from 22°C to 150°C. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the effect of thermal expansion on the shape of a material?

A: The effect of thermal expansion on the shape of a material is that it will change its shape, area, or volume in response to a change in temperature. This means that a material will expand or contract in response to a change in temperature, which can cause it to change its shape or size.

Q: How does the coefficient of volume expansion affect the change in volume of a material?

A: The coefficient of volume expansion affects the change in volume of a material by determining the rate at which the material expands or contracts in response to a change in temperature. A higher coefficient of volume expansion means that a material will expand or contract more rapidly in response to a change in temperature.

Q: What are some real-world applications of thermal expansion?

A: Some real-world applications of thermal expansion include the design of buildings, bridges, and other structures that must withstand changes in temperature, as well as the development of materials that can withstand extreme temperatures. For example, the expansion and contraction of materials due to temperature changes can cause problems in the construction of buildings and bridges, and can also affect the performance of electronic devices.

Q: How can thermal expansion be minimized or controlled?

A: Thermal expansion can be minimized or controlled by using materials with low coefficients of volume expansion, or by designing structures that can accommodate the expansion and contraction of materials due to temperature changes. For example, buildings and bridges can be designed with expansion joints that allow for the expansion and contraction of materials due to temperature changes.

Q: What is the difference between thermal expansion and thermal contraction?

A: Thermal expansion and thermal contraction are two related but distinct phenomena. Thermal expansion occurs when a material expands in response to a rise in temperature, while thermal contraction occurs when a material contracts in response to a fall in temperature. Both phenomena are important to consider in the design and construction of structures that must withstand changes in temperature.

Q: Can thermal expansion be used to create new materials or technologies?

A: Yes, thermal expansion can be used to create new materials or technologies. For example, materials with high coefficients of volume expansion can be used to create devices that can expand or contract in response to changes in temperature, such as thermoelectric devices. Additionally, the study of thermal expansion has led to the development of new materials and technologies, such as shape-memory alloys and thermochromic materials.

Q: How can thermal expansion be measured or monitored?

A: Thermal expansion can be measured or monitored using a variety of techniques, including thermometry, dilatometry, and interferometry. These techniques can be used to measure the change in length or volume of a material in response to a change in temperature, and can provide valuable information about the thermal expansion properties of a material.

In this article, we have answered some frequently asked questions related to the effects of temperature change on a thin spherical shell of silver. We have discussed the concept of thermal expansion, the coefficient of volume expansion, and some real-world applications of thermal expansion. We have also provided information on how thermal expansion can be minimized or controlled, and how it can be measured or monitored.

  • [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
  • [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
  • [3] Callen, H. B. (1985). Thermodynamics: an introduction to the physical theories of equilibrium thermodynamics. John Wiley & Sons.

This article has provided a comprehensive overview of the effects of temperature change on a thin spherical shell of silver. We have discussed the concept of thermal expansion, the coefficient of volume expansion, and some real-world applications of thermal expansion. We have also provided information on how thermal expansion can be minimized or controlled, and how it can be measured or monitored.

The study of thermal expansion is an important area of research, with many practical applications in fields such as engineering, materials science, and physics. By understanding the effects of temperature change on materials, we can design and develop new materials and technologies that can withstand extreme temperatures and provide valuable information about the thermal expansion properties of materials.

  • What are some other real-world applications of thermal expansion?
  • How can thermal expansion be used to create new materials or technologies?
  • What are some common mistakes to avoid when measuring or monitoring thermal expansion?
  • Some other real-world applications of thermal expansion include the design of electronic devices, the development of materials for aerospace applications, and the creation of devices that can detect changes in temperature.
  • Thermal expansion can be used to create new materials or technologies by designing materials with specific thermal expansion properties, such as shape-memory alloys or thermochromic materials.
  • Some common mistakes to avoid when measuring or monitoring thermal expansion include using inadequate measurement techniques, failing to account for thermal expansion in the design of experiments, and neglecting to consider the effects of temperature changes on the measurement system.