6. Find the dimensions of
fa) the specific heat capacity c,
Q=mc(T2-T ),
Answers
Answer:
Explanation:
(a) ∵ Heat Energy(Q) = m × c × Δt
where, m = mass of the body, c = specific heat capacity and Δt is the change in temperature.
∴ c = Q/mΔt
Unit of Heat = Joule.
= N × m.
= kg ms⁻² × m
= kg m² s⁻²
∴ Dimension of Q = M L² T⁻²
Now, Let us finding the Dimensions of Specific Heat Capacity.
∴ [c] = (M L² T⁻²) ÷ (M K)
[Since, the Dimension of Temperature is K]
[c] = L² T⁻² K⁻¹
Hence, the Dimensions of Specific Heat Capacity c is L² T⁻² K⁻¹.
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(b) ∵ α = (L₁ - L₂)/L₀(T₂ -T₁)
∴ Dimension of α = L/LK
= K⁻¹
Hence, the Dimension of Coefficient of Linear Expansion is K⁻¹.
(c) ∵ PV = nRT
where, R is the gas constant,n is the number of moles in the sample of gas,P is the Pressure, V is the Volume of the Gas, & T is the Temperature.
∴ R = PV/nT
For the Dimension of Pressure,
∵ Pressure = Force/Area.
= Mass × Acceleration/Area
= M × L T⁻²/L²
= M L⁻¹ T⁻²
Dimension of Volume = L³
[∵ Volume = (Length)³ ]
Dimension of Temperature = K
Dimension of n = mol.
Now,
Dimension of Gas Constant R = [(M L⁻¹ T⁻²) × (L³)] ÷ (mol)K
= M L² T⁻² K⁻¹ mol¹⁻.
Hence, the Dimension of the Gas Constant R is M L² T⁻² K⁻¹ mol¹⁻.