Question:
Dimensions of Stefan’s constant is:
Dimensions of Stefan’s constant is:
Show Hint
Stefan constant = power per unit area per \(T^4\), so no length term remains.
Updated On: Apr 16, 2026
- \( [ML^{-1}T^{-3}\theta^{-4}] \)
- \( [MT^{-3}\theta^{-4}] \)
- \( [M^2T^{-3}\theta^{-4}] \)
- \( [M^2T^{-2}\theta^{-4}] \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Stefan–Boltzmann law:
\[
E = \sigma T^4
\]
where \(E\) is energy radiated per unit area per unit time (i.e., power per unit area).
Step 1: Dimensions of \(E\).
\[ E = \frac{\text{Energy}}{\text{Area} \cdot \text{Time}} = \frac{[ML^2T^{-2}]}{[L^2 \cdot T]} = [MT^{-3}] \]
Step 2: Dimensions of \(\sigma\).
\[ \sigma = \frac{E}{T^4} = \frac{[MT^{-3}]}{\theta^4} = [MT^{-3}\theta^{-4}] \]
Step 1: Dimensions of \(E\).
\[ E = \frac{\text{Energy}}{\text{Area} \cdot \text{Time}} = \frac{[ML^2T^{-2}]}{[L^2 \cdot T]} = [MT^{-3}] \]
Step 2: Dimensions of \(\sigma\).
\[ \sigma = \frac{E}{T^4} = \frac{[MT^{-3}]}{\theta^4} = [MT^{-3}\theta^{-4}] \]
Was this answer helpful?
0
0
Top MET Physics Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $ \theta =10^{\circ} $ with respect to horizontal. The tension in the rope at its midpoint between the walls is
- At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
View More Questions
Top MET radiation Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions