# Question 897e7

May 30, 2017

${360.}^{\circ} \text{C}$

#### Explanation:

You can't answer this question without knowing the specific heat of iron

${c}_{\text{iron" = "0.45 J g"^(-1)""^@"C}}^{- 1}$

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

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

In your case, the specific heat of iron tells you that in order to increase the temperature of $\text{1 g}$ of iron by ${1}^{\circ} \text{C}$, you need to provide it with $\text{0.45 J}$ of heat.

Use this value to determine the amount of heat needed to increase the temperature of $\text{445 g}$ of iron by ${1}^{\circ} \text{C}$

445 color(red)(cancel(color(black)("g"))) * "0.45 J"/(1color(red)(cancel(color(black)("g"))) * 1^@"C") = "200.25 J"^@"C"^(-1)

So, you now know that if you add $\text{200.25 J}$ of heat to '445 g"# of iron, you will increase its temperature by ${1}^{\circ} \text{C}$.

This implies that $\text{65,100 J}$ of heat will increase the temperature of $\text{445 g}$ of iron by

$\text{65,100" color(red)(cancel(color(black)("J"))) * overbrace( (1^@"C")/(200.25color(red)(cancel(color(black)("J")))))^(color(blue)("for 445 g of iron")) = 325^@"C}$

Therefore, the final temperature of the piece of iron will be

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{final temperature" = 35.0^@"C" + 325^@"C" = 360.^@"C}}}}$

The answer is rounded to three sig figs, no decimal places.