# How much heat is required to raise the temperature of a 50.0 g block of iron by 10.0^@"C" ? Specific heat of iron: "0.449 J/g"""^@"C"

Sep 15, 2016

$\text{225 J}$

#### Explanation:

The key to this problem is the specific heat of iron, which is said to be equal to

${c}_{\text{iron" = "0.449 J g"^(-1)""^@"C}}^{- 1}$

As you know, the specific heat of a substance tells you how much heat is needed to raise the temperature of a sample of $\text{1 g}$ by ${1}^{\circ} \text{C}$.

Keep in mind that this represents the amount of heat needed per gram, per degree Celsius!

So, how much heat would be needed to increase the temperature of a $\text{50.0 g}$ block of iron by ${1}^{\circ} \text{C}$ ?

50.0 color(red)(cancel(color(black)("g"))) * overbrace("0.449 J" /(1color(red)(cancel(color(black)("g"))) ""^@"C"))^(color(blue)("the specific heat of iron")) = "22.45 J" ""^@"C"^(-1)

This means that in order to increase the temperature of $\text{50.0 g}$ of iron by ${1}^{\circ} \text{C}$ you need to provide it with $\text{22.45 J}$ of heat.

You can thus say that in order to increase the temperature of the block by ${10.0}^{\circ} \text{C}$, you must provide ten times as much heat

10.0 color(red)(cancel(color(black)(""^@"C"))) * overbrace("22.45 J"/(1color(red)(cancel(color(black)(""^@"C")))))^(color(blue)("for 50.0 g of iron")) = color(green)(bar(ul(|color(white)(a/a)color(black)("225 J")color(white)(a/a)|)))

The answer is rounded to three sig figs.