Question

The temperature of a piece of copper with a mass of 95.4 g increases from 25°C to 48°C when the metal absorbs 849 J of heat. What is the specific heat of copper?

Answer 1

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

Explanation:

A substance's specific heat tells you how much heat much be provided to increase the temperature of `"1 g"` of that substance by `1^@"C"`.

The equation that establishes a relationship between how much heat a substance must absorb in order to register a change in its temperature looks like this

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

`q` - the amount of heat absorbed
`m` - the mass of the sample
`c` - the specific heat of the substance
`DeltaT` - the change in temperature, defined as the difference betwen the final temperature and the nitial temperature

In your case, you know that the temperature of `"95.4-g"` sample of copper increases from `25` to `48^@"C"` after absorbing `"849 J"` worth of heat.

Rearrange the equation to solve for `c` and plug in your values

`c = q/(m * DeltaT)`

`c = "849 J"/("95.4 g" * (48-25)^@"C") = 0.38693"J"/("g" ""^@"C")`

Rounded to two sig figs, the number of sig figs you ahve for the two temperatures of the copper sample, the answer will be

`c = color(green)(0.39"J"/("g" ""^@"C"))`

It's worth noting that the result matches listed values almost perfectly

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