# A sample of an unknown metal has a mass of 120.7 g. As the sample cools from 90.5 °C to 25.7 °C, it releases 7020 J of energy. What is the specific heat of the sample?

Dec 18, 2015

c = 0.898"J"/("g" ""^@"C")

#### Explanation:

As you know, a substance's specific heat tells you how much heat must be absorbed or lost in order for $\text{1 g}$ of that substance to experience a ${1}^{\circ} \text{C}$ temperature change.

The equation that establishes a relationship between heat absorbed / lost and change in temperature looks like this

$\textcolor{b l u e}{q = m \cdot c \cdot \Delta T} \text{ }$, where

$q$ - heat absorbed/lost
$m$ - the mass of the sample
$c$ - the specific heat of the substance
$\Delta T$ - the change in temperature, defined as final temperature minus initial temperature

Now, it is important to realize that the value of $q$ must come out negative for samples that experience a decrease in temperature.

From a thermodynamic point of view, heat lost always carries a negative sign, so you need to keep that in mind when plugging in your values.

Simply put, when $\text{7020 J}$ of energy are released, the heat lost is written as

$q = - \text{7020 J}$

With this being said, plug in your values into the above equation and solve for $c$, the specific heat of the metal

$q = m \cdot c \cdot \Delta T \implies c = \frac{q}{m \cdot \Delta T}$

$c = \left(- \text{7020 J")/("120.7 g" * (25.7 - 90.5)^@"C}\right)$

$c = \left(\textcolor{red}{\cancel{\textcolor{b l a c k}{-}}} \text{7020 J")/(color(red)(cancel(color(black)(-)))"7821.36 g" ""^@"C") = 0.8975 "J"/("g" ""^@"C}\right)$

Rounded to three sig figs, the number of sig figs you have for the two temperatures of the metal, the answer will be

c = color(green)(0.898"J"/("g" ""^@"C"))