Question

A 0.050g ball of aluminum foil absorbs 1.42 J heat when it is heated 31.6°C. What is the specific heat of aluminum foil?

Answer 1

`"0.899 J g"^(-1)""^@"C"^(-1)`

Explanation:

A substance's specific heat tells you the amount of heat needed to increase the temperature of `"1 g"` of that substance by `1^@"C"`.

In your case, you know that the temperature of `"0.050 g"` of aluminium increased by `31.6^@"C"` upon the absorption of `"1.42 J"` of heat.

The first thing to do here is to figure out how much heat is needed to increase the temperature of `"1 g"` of aluminium by `31.6^@"C"`.

`1 color(red)(cancel(color(black)("g"))) * "1.41 J"/(0.050color(red)(cancel(color(black)("g")))) = "28.4 J"`

This is how much heat is needed to cause a `31.6^@"C"` increase in the temperature of `"1 g"` of aluminium. Now all you have to do is calculate how much heat is needed to increase the temperature of `"1 g"` by `1^@"C"`

`1 color(red)(cancel(color(black)(""^@"C"))) * "28.4 J"/(31.6color(red)(cancel(color(black)(""^@"C")))) = "0.899 J"`

Therefore, the specific heat of aluminium will be

`color(green)(|bar(ul(color(white)(a/a)color(black)(c_"Al" = "0.899 J g"^(-1)""^@"C"^(-1))color(white)(a/a)|)))`

The answer is rounded to three sig figs.

`color(white)(a/a)`

ALTERNATIVELY

You can get the same result by suing the following equation

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

`q` - the amount of heat released
`m` - the mass of the sample
`c` - the specific heat of the substance
`DeltaT` - the change in temperature, defined as the difference between the final temperature and the initial temperature

In your case, the change in temperature is equal to

`DeltaT = 31.6^@"C"`

You will have

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

Plug in your values to find

`c_"Al" = "1.42 J"/("0.050 g" * 31.6^@"C") = color(green)(|bar(ul(color(white)(a/a)color(black)("0.899 J g"^(-1)""^@"C"^(-1))color(white)(a/a)|)))`

The listed value for the specific heat of aluminium is

`c_"Al" = "0.900 J g"^(-1)""^@"C"^(-1)`

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/sphtt.html