Deduce the dimensional formulae for the following physical quantities : (i) Specific heat (ii) Entrophy (iii) Thermal conductivity (iv) Stepan's constant (v) Boltzmann's constant (vi) Universal gas constant.

Deduce the dimensional formulae for the following physical quantities

1.	Deduce the dimensional formulae for the following physical quantities : (i) Specific heat (ii) Entrophy (iii) Thermal conductivity (iv) Stepan's constant (v) Boltzmann's constant (vi) Universal gas constant.
Answer» Solution :(i) Specific HEAT `=("Heat")/("Mass" xx "Temperature")` `=("Work")/("Mass" xx "Temperature")` `=("Force" xx "distance")/("Mass" xx "Temperature")=([MLT^(-2)][L])/([M][K])` `=[M^(0)L^(2)T^(-2)K^(-1)]` (II) ENTROPY `=("Heat")/("Temperature")=([ML^(2)T^(-2)])/([K])` `=[ML^(2)T^(-2)K^(-1)]` (iii) Thermal conductivity `=("Heat"xx "Distance")/("Area"xx"Temperature"xx"Time")` `=([ML^(2)T^(-2)][L])/([L^(2)][K][T])` `=MKT^(-3)K^(-1)` (IV) Stefan.s constant `=("Energy")/("Area"xx"Time"xx("temperature")^(4))` `=([ML^(2)T^(-2)])/([L^(2)][T][K]^(4))` `=[ML^(0)T^(-3)K^(-4)]` (v) Boltzmann.s constant `=("Energy")/("Temperature")` `=([ML^(2)T^(-2)])/([K])` `=[ML^(2)T^(-2)K^(-1)]` (vi) Universal gas constant `=("Pressure"xx"Volume")/("No. of moles" xx "Temperature")` `=(PV)/(nT)` `=([ML^(-1)T^(-2)][L^(3)])/(["mol.][K])` `=[ML^(2)T^(-2)K^(-1) "mol"^(-1)]`