# What quantity of heat energy must have been applied to a block of aluminum weighing 42.7 g if the temperature of the block of aluminum increased by 15.2°C?

##### 1 Answer

#### Explanation:

As it stands, the problem fails to provide you with an essential piece of information - the value of aluminium's **specific heat**.

This means that you're going to have to track it yourself. You can find it listed here

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

as being equal to

#c = "0.91 J g"^(-1)""^@"C"^(-1)#

So, a substance's **specific heat** tells you how much heat is needed in order to increase the temperature of

In this case, you need to provide aluminium with

You know that the block of aluminium has a mass **by just**

#42.7 color(red)(cancel(color(black)("g"))) xx "0.91 J" color(red)(cancel(color(black)("g"^(-1))))""^@"C"^(-1) = "38.86 J" ""^@"C"^(-1)#

This much heat would increase the temperature of **times** more heat

#15.2color(red)(cancel(color(black)(""^@"C"))) xx "38.86 J" color(red)(cancel(color(black)(""^@"C"^(-1)))) = "590.67 J"#

Rounded to three **sig figs**, the answer will be

#"heat needed" = color(green)(|bar(ul(color(white)(a/a)"591 J"color(white)(a/a)|)))#

**Alternatively**, you can use the formula

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

*change in temperature*

Plug in your values to get

#q = 42.7 color(red)(cancel(color(black)("g"))) * "0.91 J" color(red)(cancel(color(black)("g"^(-1))))color(red)(cancel(color(black)(""^@"C"^(-1)))) * 15.2color(red)(cancel(color(black)(""^@"C")))#

#q = color(green)(|bar(ul(color(white)(a/a)"591 J"color(white)(a/a)|)))#