# Question #5dc43

##### 1 Answer

#### Explanation:

The key to this problem is aluminium's **specific heat**, which tells you how much heat is needed to increase the temperature of

Aluminium's specific heat is said to be equal to

Now, let's *assume* that your sample has a mass of

#DeltaT = 187^@"C" - 65^@"C" = 122^@"C"#

you would need to provide it with **times more heat** than what would be needed to increase its temperature by

More specifically, you would need to provide it with

#122color(red)(cancel(color(black)(""^@"C"))) * overbrace("0.897 J"/(1color(red)(cancel(color(black)(""^@"C")))))^(color(purple)("heat needed for"color(white)(a)1^@"C"color(white)(a) "increase for 1 g of Al")) = "109.434 J"#

However, you end up adding **not** equal to

The ratio between the heat added to the sample to get its temperature to increase by **mass of the sample**, expressed in *grams*

#1650color(red)(cancel(color(black)("J"))) * overbrace("1 g"/(109.434color(red)(cancel(color(black)("J")))))^(color(purple)("heat needed for"color(white)(a) 122^@"C" color(white)(a)"increase for 1 g of Al")) = "15.08 g"#

Expressed in *kilograms* and rounded to two **sig figs**, the answer will be

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 kg" 1= 10^3"g")color(white)(a/a)|)))#

#"mass of Al" = color(green)(|bar(ul(color(white)(a/a)"0.015 kg"color(white)(a/a)|)))#

**ALTERNATIVE SOLUTION**

You can get the same result by using the formula

#color(blue)(|bar(ul(color(white)(a/a)q = m * c * DeltaTcolor(white)(a/a)|)))" "# , where

*change in temperature*

Rearrange to solve for

#q = m * c * DeltaT implies m = q/(c * DeltaT)#

Plug in your values to get

#m = (1650 color(red)(cancel(color(black)("J"))))/(0.897color(red)(cancel(color(black)("J"))) "g" color(red)(cancel(color(black)(""^@"C"^(-1)))) * (187 - 65)color(red)(cancel(color(black)(""^@"C"))))#

#m = "15.08 g"#

Once again, you'll have

#"mass of Al" = color(green)(|bar(ul(color(white)(a/a)"0.015 kg"color(white)(a/a)|)))#