TS EAMCET · Physics · Work Power Energy

The dimensions of $σ b^{4}$ where $' σ'$ is Stefan's constant and $' b'$ is Wien's constant are

A $[M^{0} L^{0} T^{0}]$
B $[{ML}^{4} T^{- 3}]$
C $[{ML}^{- 2} T]$
D $[{ML}^{6} T^{- 3}]$

Verified Solution

Answer & Solution

Correct Answer

(B) $[{ML}^{4} T^{- 3}]$

Step-by-step Solution

Detailed explanation

According to Stefan's law, the energy E emitted per unit area per unit time is, E=σT4 …(1) where, σ is Stefan's constant and, T is the temperature. The dimensional equation for above, ML2T-2L2T=σK4. So, σ=ML2T-2L2T1K4 ⇒σ=ML0T-3K-4…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match the following

	Column-I		Column-II
(A)	Shear modulus	(I)	Resistance to change in volume
(B)	Shearing stress	(II)	Proportionality constant
(C)	Elastic fatigue	(III)	Tangential stress
(D)	Modulus of elasticity	(IV)	Temporary loss of elastic property
		(V)	Resistance to change against deformation force

The correct match is

TS EAMCET 2022 Easy

Explore more questions on app

From TS EAMCET

Explore more questions on app

The dimensions of σb4 where 'σ' is Stefan's constant and 'b' is Wien's constant are

Step-by-step Solution

The dimensions of $σ b^{4}$ where $' σ'$ is Stefan's constant and $' b'$ is Wien's constant are