# What is the specific heat capacity of silver atom, if "386 g" of "Ag" has a heat capacity of "91.5 J/"^@ "C"?

Jun 30, 2017

This is just asking you to know what the units of specific heat capacity, $s$, are. After that, this should take you less than a minute:

$\textcolor{b l u e}{{s}_{A g}} = \left(\text{91.5 J/"^@ "C")/("386 g Ag") = color(blue)("0.237 J/g"^@ "C}\right)$

So, every gram of silver metal that you have at room temperature and $\text{1 atm}$ pressure will take $\text{0.237 J}$ of energy input to heat up by ${1}^{\circ} \text{C}$.

What we can take away from this is that the specific heat capacity is an intensive property; it does not depend on the amount of substance you have, because it is defined for every gram of substance.

(The units already account for how much mass the quantity pertains to.)

However, heat capacity is an extensive property. The more substance you have, the higher its heat capacity will be.

If you had $\text{1000 g}$ of silver metal, what would be its heat capacity in $\text{J/"^@ "C}$? Well, it should be $\frac{1000}{386} = 2.59$ times what you were given in this question in $\text{J/"^@ "C}$.