Q1.6: HC Verma: Concepts of Physics - Volume 1 Introduction to physics 1.6 Solution: Question 6: Find the dimensions of (a) Specific heat…
Students often omit the molar unit (mol) in the dimensions of the gas constant $R$, treating it as a pure number. Remember that $n$ in $PV=nRT$ is measured in moles, so the dimension of $R$ must explicitly include $(mol)^{-1}$ to ensure dimensional homogeneity.
Question 6: Find the dimensions of
(a) Specific heat capacity c
(b) Coefficient of linear expansion α
(c) Gas constant R.
Some of the equations used here are - q = mc(T₂ - T₁), Lₜ = L₀[1 + α(T₂ - T₁)] and PV = nRT
Step-by-Step Verified Solution
(a) Dimensions of specific heat capacity (c):
c = Q / (mΔT) = [ML²T⁻²] / ([M][K]) = [L²T⁻²K⁻¹]
(b) Dimensions of coefficient of linear expansion (α):
α = (L₁ - L₂) / (L₀ΔT) = [L] / ([L][K]) = [K⁻¹]
(c) Dimensions of gas constant (R):
R = PV / (nT) = ([ML⁻¹T⁻²][L³]) / ([mol][K]) = [ML²T⁻²K⁻¹(mol)⁻¹]