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 = [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 =


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