# How many joules of heat are needed to raise the temperature of 10.0 g of aluminum from 22°C to 55°C, if the specific heat of aluminum is 0.90 J/g°C?

##### 1 Answer

#### Explanation:

The key to this problem lies with aluminium's specific heat, which as you know tells you how much heat is needed in order to increase the temperature of

In your case, aluminium is said to have a specific heat of

*So, what does that tell you?*

In order to increase the temperature of

But remember, this is how much you need to provide **for every gram** of aluminium in order to increase its temperature by

#underbrace(overbrace("0.90 J")^(color(blue)("1 gram")) + overbrace("0.90 J")^(color(blue)("1 gram")) + " ... " + overbrace("0.90 J")^(color(blue)("1 gram")))_(color(red)("10 times")) = 10 xx "0.90 J"#

However, you don't want to increase the temperature of the sample by

#DeltaT = 55^@"C" - 22^@"C" = 33^@"C"#

This means that you're going to have to use that much heat **for every degree Celsius** you want the temperature to change. You can thus say that

#underbrace(overbrace(10 xx "0.90 J")^(color(purple)(1^@"C")) + overbrace(10 xx "0.90 J")^(color(purple)(1^@"C")) + " ... " + overbrace(10 xx "0.90 J")^(color(purple)(1^@"C")))_(color(red)("33 times")) = 33 xx 10 xx "0.90 J"#

Therefore, the **total amount of heat** needed to increase the temperature of

#q = 10.0 color(red)(cancel(color(black)("g"))) * 0.90"J"/(color(red)(cancel(color(black)("g"))) color(red)(cancel(color(black)(""^@"C")))) * 33color(red)(cancel(color(black)(""^@"C")))#

#q = color(green)("297 J")#

I'll leave the answer rounded to three sig figs, despite the fact that your values only justify two sig figs.

For future reference, this equation will come in handy

#color(blue)(q = m * c * DeltaT)" "# , where

*final temperature* and the *initial temperature* of the sample