# Question c1168

Mar 18, 2017

$\text{2464 J}$

#### Explanation:

The key to this problem is the specific heat of the metal.

You know that copper has a specific heat of

${c}_{\text{copper" = "0.3850 J g"^(-1)""^@"C}}^{- 1}$

This tells you that in order to increase the temperature of $\text{1 g}$ of copper by ${1}^{\circ} \text{C}$, you need to provide it with $\text{0.3850 J}$ of heat.

Now, how much energy would be needed in order to increase the temperature of $\text{715.0 g}$ of copper by just ${1}^{\circ} \text{C}$ ? Use the specific heat as a conversion factor to get

715.0 color(red)(cancel(color(black)("g"))) * overbrace("0.3850 J"/(1color(red)(cancel(color(black)("g"))) * 1^@"C"))^(color(blue)("the specific heat of copper")) = "275.275 J"^@"C"^(-1)#

Since you know that you need $\text{275.275 J}$ of heat in order to increase the temperature of $\text{715.0 g}$ of copper by ${1}^{\circ} \text{C}$, you can say that in order to increase its temperature by

${22.46}^{\circ} \text{C" - 13.51^@"C" = 8.95^@"C}$

you will need to provide

$8.95 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{^@"C"))) * "275.275 J"/(1color(red)(cancel(color(black)(""^@"C")))) = color(darkgreen)(ul(color(black)("2464 J}}}}$

The answer is rounded to four sig figs.