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 
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 = [ML2T-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 (lt) = initial length (l0)[1 + α(ΔT)]
where ΔT is the change in temperature
From the relation we have 
Dimensions of lt = [L]
Dimensions of l0 = [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 (Kb). 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-1T-2]
Dimensions of V = [L3]
Dimensions of n = [mol]
Dimensions of T = [K]
Dimensions of R = 