Question
Physics Question on physical world
Dimensional formula of Stefan's constant is
A
[MT-3K-4]
B
[MLT-2K-4]
C
[ML2T-2]
D
[MT-2L0]
Answer
[MLT-2K-4]
Explanation
Solution
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 dimensionsof 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].
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