Question

A student asserts that a suitable unit for specific heat is $\mathbf{1}{\mathbf{m}}^{\mathbf{2}}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}\mathbf{-}\mathbf{C}\mathbf{°}$. Is she correct? Why or why not?

Short answer

The student asserts that a suitable unit for specific heat is $1{\mathrm{m}}^2/{\mathrm{s}}^2.°\mathrm{C}$. She is correct.

Step-by-step solution

Given data

The student asserted the unit for specific heat as $1{\mathrm{m}}^2/{\mathrm{s}}^2.°\mathrm{C}$.

Understanding specific heat  

Unit for specific heat is given as,

$\frac{\mathrm{J}}{\mathrm{kg}.°\mathrm{C}}$

Let's convert it into the given asserted unit as,

$$\begin{gathered} =\frac{1\mathrm{J}}{1\mathrm{kg}.°\mathrm{C}}\times \frac{1\mathrm{kg}.{\mathrm{m}}^2/{\mathrm{s}}^2}{1\mathrm{J}} \\ =\frac{1{\mathrm{m}}^2/{\mathrm{s}}^2}{1°\mathrm{C}} \\ =1{\mathrm{m}}^2/{\mathrm{s}}^2.°\mathrm{C} \end{gathered}$$

Thus, the student asserts that a suitable unit for specific heat is $1{\mathrm{m}}^2/{\mathrm{s}}^2.°\mathrm{C}$. She is correct.