Question

The specific heat capacity of a particular solid material at temperature close 0k is given by c=aT³. What is the S.I unit of the constant where T=temperature

Answer 1

The SI unit of specific heat capacity is $Jkg^{-1}K^{-1}$. The dimensions on both side of the expression $c = aT^3$ must be equal. Therefore, the SI unit of constant $a$ is:

$$[a] = Jkg^{-1}K^{-4} = kgm^2s^{-2}kg^{-1}K^{-4} = m^2s^{-2}K^{-4}.$$

Answer:

$[a] = m^2s^{-2}K^{-4}.$