# Question a5ef6

Jan 14, 2018

${\text{0.0299 cal g"^(-1)""^@"C}}^{- 1}$

#### Explanation:

The specific heat of a substance tells you the amount of energy required to increase the temperature of $\text{1 g}$ of that substance by ${1}^{\circ} \text{C}$.

In your case, you know that in order to increase the temperature of $\text{26.0 g}$ of an unknown substance by ${250}^{\circ} \text{C}$, you need to provide $\text{194.0 cal}$ of heat.

Keep in mind that in order to be able to calculate the specific heat of the substance using the information provided by the problem, you must assume that the state of the substance does not change upon heating.

So, the first thing that you must calculate here is the amount of heat needed to increase the temperature of $\text{1 g}$ of this substance by ${250}^{\circ} \text{C}$.

1 color(red)(cancel(color(black)("g"))) * overbrace("194.0 cal"/(26.0 color(red)(cancel(color(black)("g")))))^(color(blue)("for a 250-"^@"C increase")) = "7.4615 cal"

This tells you that in order to increase the temperature of $\text{1 g}$ of this substance by ${250}^{\circ} \text{C}$, you need to supply $\text{7.4615 cal}$ of heat.

You can thus say that in order to increase the temperature of $\text{1 g}$ of this substance by ${1}^{\circ} \text{C}$, you need

1 color(red)(cancel(color(black)(""^@"C"))) * "7.4615 cal"/(250color(red)(cancel(color(black)(""^@"C")))) = "0.02985 cal"#

The specific heat of the substance is equal to

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{specific heat = 0.0299 cal g"^(-1)""^@"C}}^{- 1}}}}$

You need $\text{0.0299 cal}$ to increase the temperature of $\text{1 g}$ of this substance by ${1}^{\circ} \text{C}$.

The answer is rounded to three sig figs.