JEE Main 2024 · 6 April · evening · Single correct · +4 / −1
Given below are two statements:
Statement (I) : Dimensions of specific heat is [L² T⁻² K⁻¹].
Statement (II) : Dimensions of gas constant is [M L² T⁻¹ K⁻¹].
In the light of the above statements, choose the most appropriate answer from the options given below.
- (a) Statement (I) is incorrect but statement (II) is correct
- (b) Both statement (I) and statement (II) are incorrect
- (c) Both statement (I) and statement (II) are correct
- (d) Statement (I) is correct but statement (II) is incorrect
Answer and solution
Answer (d) Statement (I) is correct but statement (II) is incorrect
Solution
Physics sir · 4 steps
Write each quantity as energy divided by something, and the dimensions fall straight out.
- Specific heat. From Q = mc Δ T, we get c = Q/(m Δ T). Heat is energy, with dimensions [M L² T⁻²].
[c] = [M L² T⁻²]/[M][K] = [L² T⁻² K⁻¹]
- Statement I. The mass cancels and the result matches exactly, so Statement I is correct.
- Gas constant. From PV = nRT, we get R = PV/nT. Here PV is energy, [M L² T⁻²], so [R] = [M L² T⁻² K⁻¹ mol⁻¹]. Statement II has T⁻¹ instead of T⁻², so it is incorrect.
- So. Statement I is correct and Statement II is incorrect, which is option (d).
The idea to keep. Specific heat, gas constant, Boltzmann constant: all are energy per something. Start from energy [M L² T⁻²] and divide by whatever sits below it.
Answer from the NTA final answer key. Solution by PrepWiser.