Question

How do you calculate the specific heat capacity of a piece of wood if 1500.0 g of the wood absorbs `6.75 * 10^4` joules of heat, and its temperature changes from 32°C to 57°C?

Answer 1

`1.8"J"/("g" ""^@"C")`

Explanation:

A substance's specific heat tells you how much heat much either be added or removed from `"1 g"` of that substance in order to cause a `1^@"C"` change in temperature.

The equation that establishes a relationship between specific heat, heat added or removed, and change in temperature looks like this

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

In your case, the `"1500.0-g"` piece of wood is said to absorb a total of `6.75 * 10^4"J"` of heat. This caused its temperature to increase from `32^@"C"` to `57^@"C"`.

The difference between the final temperature and the initial temperature of the sample will be the value for `DeltaT`.

`DeltaT = 57^@"C" - 32^@"C" = 25^@"C"`

This means that the specific heat of the wood is equal to

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

Plug in your values to get

`c = (6.75 * 10^4"J")/("1500.0 g" * 25^@"C") = color(green)(1.8"J"/("g" ""^@"C"))`

The answer is rounded to two sig figs, the number of sig figs you have for the two temperatures of the sample.