Dimensional formula of Stefan's constant is
Show Hint
To determine the dimensions of Stefan's constant, you can analyze the equation that relates power, area, temperature, and emissivity.
[MT-3K-4]
[MLT-2K-4]
[ML2T-2]
[MT-2L0]
The Correct Option is B
Approach Solution - 1
The dimensions of Stefan's constant can be derived from the equation for power radiated: R = σAeT
- where R is the power,
- σ is Stefan's constant,
- A is the area,
- e is the emissivity,
- T is the temperature.
The dimensions of each term are as follows:
- Power (R): [ML²T⁻³]
- Area (A): [L²]
- Temperature (T): [K]
- Emissivity (e): [dimensionless]
To find the dimensions of σ, we rearrange the equation:
σ = R / (AeT)
Substituting the dimensions of each term:
[ML²T⁻³] / ([M0L²T0] × [dimensionless] × [K4])
Simplifying:
[ML0T-³K⁻⁴]
Therefore, the dimensions of Stefan's constant (σ) are [ML0T-³K⁻⁴].
Discover More From Chapter: Units and Measurements
Approach Solution -2
The Correct Answer is (B)
Real Life Applications
The dimensional formula of Stefan's constant is [M1L0T-3K-4]. It has units of watts per square meter per kelvin to the fourth power. The real-life applications of Stefan's constant include:
1. Stefan's constant can be used to calculate the total amount of thermal radiation emitted by a star. This information can be used to determine the star's temperature, luminosity, and size.
2. Stefan's constant can be used to calculate the amount of thermal radiation that a spacecraft will absorb from the sun. This information can be used to design spacecraft that can withstand the heat of space.
3. Stefan's constant can be used to model the amount of heat that is absorbed by Earth's atmosphere. This information can be used to understand how climate change is affecting Earth's temperature.
Question can also be asked as
1. What are the dimensions of Stefan's constant?
2. How is Stefan's constant represented in terms of fundamental units?
3. What is the SI unit of Stefan's constant?
4. What is the CGS unit of Stefan's constant?
Approach Solution -3
The Correct Answer is (B)
Stefan's constant is a fundamental physical constant. It plays a crucial role in the study of thermal radiation and blackbody radiation.
- It relates the power radiated by a blackbody to its surface area, temperature, and emissivity.
- Stefan's constant, denoted as σ, is named after the Austrian physicist Josef Stefan.
- It appears in Stefan's law, which describes the power radiated by a blackbody per unit area as a function of its temperature.
Stefan's law can be expressed as follows:
R = σAeT,
- where R represents the power radiated,
- σ is Stefan's constant,
- A is the surface area,
- T is the temperature, and
- e is the emissivity of the body
The constant σ encapsulates the fundamental relationship between the power radiated by a blackbody and its other properties.
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Physical World
The physical world includes the complications of the natural world around us. It is a type of analysis of the physical world around us to understand how it works. The fundamental forces that control nature are:
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