Find the dimensions ofa the specific heat capacity c-b the coefficient of linear expansion - andc lthe gas constant R- Some of the equations involving these quatities are Q - mc T 2- T 1- l 1- l 0-1- T 2- T 1- and PV - nRT-

(a) Specific heat capacity, C = Q/m Δ T = ML^2T^ 2/[M][K] =[L^2 T^ 2 K^ 1] (b) Coefficient of linear expansion, α = L_1 L_0/L_0 Δ T = [L]/[LK] = [K^ 1] (c) Ga ...

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Byju's Answer

Standard XII

Chemistry

Relation between P, V, T, Gamma in Adiabatic Proceses

Find the dime...

Question

Find the dimensions of

(a) the specific heat capacity c,

(b) the coefficient of linear expansion $α$ and

(c) lthe gas constant R.

Some of the equations involving these quatities are $Q = m c (T_{2} - T_{1}), l_{1} = l_{0} [1 + α (T_{2} - T_{1})]$ and PV = nRT.

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Solution

(a) Specific heat capacity,

$C = \frac{Q}{m Δ T} = \frac{M L^{2} T^{- 2}}{[M] [K]}$

$= [L^{2} T^{- 2} K^{- 1}]$

(b) Coefficient of linear expansion,

$α = \frac{L_{1} - L_{0}}{L_{0} Δ T} = \frac{[L]}{[L K]} = [K^{- 1}]$

(c) Gas constant,

$R = \frac{P V}{n T} = \frac{[M L^{- 1} T^{- 2}] [L^{3}]}{[(m o l)] [K]}$

$= [M L^{2} T^{- 2} K^{- 1} (m o l)^{- 1}]$

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Q. Find the dimensions of
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Find the dimensions of (a) the specific heat capacity c, (b) the coefficient of linear expansion α and (c) lthe gas constant R. Some of the equations involving these quatities are Q=mc(T2−T1), l1=l0[1+α(T2−T1)] and PV = nRT.

(a) Specific heat capacity, C=QmΔT=ML2T−2[M][K] =[L2T−2K−1] (b) Coefficient of linear expansion, α=L1−L0L0ΔT=[L][LK]=[K−1] (c) Gas constant, R=PVnT=[ML−1T−2][L3][(mol)][K] =[ML2T−2K−1(mol)−1]

Find the dimensions of

(a) the specific heat capacity c,

(b) the coefficient of linear expansion $α$ and

(c) lthe gas constant R.

Some of the equations involving these quatities are $Q = m c (T_{2} - T_{1}), l_{1} = l_{0} [1 + α (T_{2} - T_{1})]$ and PV = nRT.