Q: Specific heat of hydrogen at constant pressure is 29 J/K/mole. If unit of length is changed to 50 cm, unit of time is changed to 2 s and unit of temperature is changed to 2 K, keeping unit of a mass and amount of substance unchanged, the value of specific heat of hydrogen would be

(a) 928 new units

(b) 58 new units

(c) 92.8 new units

(d) 9280 new units

Ans: (a)

Unit of $\displaystyle c_p = (Joule)(kelvin)^{-1}(mole)^{-1} $

Dimensional formula of $\displaystyle c_p = [M L^2 T^{-2}] [K]^{-1}[mole]^{-1} $

The value of specific heat of hydrogen $\displaystyle = 29 \times \frac{Dimension \; of \; old \; System}{Dimension \; of \; new \; System}$

The value of specific heat of hydrogen $\displaystyle = 29 \times \frac{[M L^2 T^{-2}] [K]^{-1}[mole]^{-1}}{[M (L/2)^2 (2T)^{-2}] [2K]^{-1}[mole]^{-1}}$

= 928