# Question 4719e

Mar 15, 2017

$\text{69.0 g}$

#### Explanation:

Your tool of choice here will be this equation

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{q = m \cdot c \cdot \Delta T}}}$

Here

• $q$ is the heat lost or gained by the substance
• $m$ is the mass of the sample
• $c$ is the specific heat of the substance
• $\Delta T$ is the change in temperature, defined as the difference between the final temperature and the initial temperature of the sample

As you know, the specific heat of copper is listed as

${c}_{\text{copper" = "0.385 J g"^(-1)""^@"C}}^{- 1}$

http://www2.ucdsb.on.ca/tiss/stretton/database/specific_heat_capacity_table.html

So, the problem wants you to determine the mass of copper that would undergo a ${35.5}^{\circ} \text{C}$ increase in temperature upon the addition of $\text{943.06 J}$.

The temperature of the sample increases by ${35.5}^{\circ} \text{C}$, so you can say that

$\Delta T = {35.5}^{\circ} \text{C}$

Rearrange the equation to isolate $m$ on one side

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

Plug in your values to find

m = (943.06 color(red)(cancel(color(black)("J"))))/(0.385 color(red)(cancel(color(black)("J"))) "g"^(-1) color(red)(cancel(color(black)(""^@"C"^(-1)))) * 35.5 color(red)(cancel(color(black)(""^@"C")))) = color(darkgreen)(ul(color(black)("69.0 g")))

The answer is rounded to three sig figs.

This means that if you supply $\text{943.06 J}$ of heat to $\text{69.0 g}$ of copper, you will cause its temperature to increase by ${35.5}^{\circ} \text{C}$.

$\textcolor{w h i t e}{\frac{a}{a}}$

ALTERNATIVE APPROACH

You can get the same result by using the specific heat of the metal, which tells you that in order to increase the temperature of $\text{1 g}$ of copper by ${1}^{\circ} \text{C}$, you need to supply it with $\text{0.385 J}$ of energy.

Start by calculating the amount of energy needed to increase the temperature of $\text{1 g}$ of copper by ${35.5}^{\circ} \text{C}$

35.5 color(red)(cancel(color(black)(""^@"C"))) * "0.385 J"/("1 g" * 1color(red)(cancel(color(black)(""^@"C")))) = "13.6675 J g"^(-1)#

Since you know that you have $\text{943.06 J}$ available, you can use this value to find the number of grams of copper

$943.06 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{J"))) * overbrace("1 g"/(13.6675color(red)(cancel(color(black)("J")))))^(color(blue)("needed for 35.5"^@"C increase in temperature")) = color(darkgreen)(ul(color(black)("69.0 g}}}}$