Q. 64.5( 17 Votes )

# Find the dimensions of

A. the specific heat capacity c,

B. the coefficient of linear expansion α and

C. the gas constant R.

Some of the equations involving these quantities are

and

Answer :

A. Specific heat capacity is defined as the amount of heat required to raise the temperature of a body of mass 1 gm by 1 K.

Specific heat capacity can be calculated from the relation -

Heat energy (Q) = mass (m) × specific heat capacity(c) × temperature gradient(ΔT)

From here

Dimensions of Q = [ML^{2}T^{-2}]

Dimensions of m = [M]

Dimensions of ΔT = [K]

Dimensions of c =

B. Coefficient of linear expansion is defined as the rate of change of length of a body when heat is applied to it per unit temperature change.

Coefficient of linear expansion (α) can be calculated from the relation –

Length at time t (l_{t}) = initial length (l_{0})[1 + α(ΔT)]

where ΔT is the change in temperature

From the relation we have

Dimensions of l_{t} = [L]

Dimensions of l_{0} = [L]

Dimensions of ΔT = [K]

Dimensions of α =

C. Universal Gas constant is the constant of proportionality that appears in the ideal gas equation. It is also equal to the Boltzmann Constant (K_{b}). It is a physical constant that gives the kinetic energy of a gas for different temperatures.

Gas constant (R) can be found out from the ideal gas equation –

Pressure(P) × Volume(V) = moles(n)× UGC (R) × Temperature (T)

From the relation

Dimensions of P = [ML^{-1}T^{-2}]

Dimensions of V = [L^{3}]

Dimensions of n = [mol]

Dimensions of T = [K]

Dimensions of R =

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