Question

What is the specific heat of an unknown substance if 2000 J of energy are required to raise the temperature of 400 grams of the substance 45 degrees Celsius?

Answer 1

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

Explanation:

A substance's specific heat tells you how much heat is needed in order to raise the temperature of `"1 g"` of that substance by `1^@"C"`.

Your tool of choice here will be this equation

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

`q` - the amount of heat gained
`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 sample is said to have a mass of `"400 g"`. The change in temperature is said to be equal to `45^@"C"`.

You know that in order to increase the temperature of this sample by `45^@"C"`, you need to provide it with `"2000 J"` of energy, which means that its specific heat will be

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

`c = "2000 J"/("400 g" * 45^@"C") = color(green)(|bar(ul(color(white)(a/a)color(black)("0.1 J g"^(-1)""^@"C"^(-1))color(white)(a/a)|)))`

The answer is rounded to one sig fig.