# The temperature of a piece of copper with a mass of 95.4 g increases from 25°C to 48°C when the metal absorbs 849 J of heat. What is the specific heat of copper?

Oct 30, 2015

0.39"J"/("g" ""^@"C")

#### Explanation:

A substance's specific heat tells you how much heat much be provided to increase the temperature of $\text{1 g}$ of that substance by ${1}^{\circ} \text{C}$.

The equation that establishes a relationship between how much heat a substance must absorb in order to register a change in its temperature looks like this

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

$q$ - the amount of heat absorbed
$m$ - the mass of the sample
$c$ - the specific heat of the substance
$\Delta T$ - the change in temperature, defined as the difference betwen the final temperature and the nitial temperature

In your case, you know that the temperature of $\text{95.4-g}$ sample of copper increases from $25$ to ${48}^{\circ} \text{C}$ after absorbing $\text{849 J}$ worth of heat.

Rearrange the equation to solve for $c$ and plug in your values

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

c = "849 J"/("95.4 g" * (48-25)^@"C") = 0.38693"J"/("g" ""^@"C")

Rounded to two sig figs, the number of sig figs you ahve for the two temperatures of the copper sample, the answer will be

c = color(green)(0.39"J"/("g" ""^@"C"))

It's worth noting that the result matches listed values almost perfectly

http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html