Question

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?

Answer 1

`"591 J"`

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 `"1 g"` of that substance by `1^@"C"`.

In this case, you need to provide aluminium with `"0.91 J"` of heat in order to increase the temperature of `"1 g"` by `1^@"C"`.

You know that the block of aluminium has a mass `"42.7 g"`. This means that if you were to increase its temperature by just `1^@"C"`, you'd need

`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 `"42.7 g"` of aluminium by `1^@"C"`. To increase its temperature by `15.2^@"C"`, you'd need `15.2` 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

`q` - the amount of heat added / removed
`m` - the mass of the sample
`c` - the specific heat of the substance
`DeltaT` - the 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)|)))`