Question

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"`

Answer 1

`"225 J"`

Explanation:

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

`c_"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 `"1 g"` by `1^@"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 `"50.0 g"` block of iron by `1^@"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 `"50.0 g"` of iron by `1^@"C"` you need to provide it with `"22.45 J"` of heat.

You can thus say that in order to increase the temperature of the block by `10.0^@"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.