Question

How do you determine the specific heat of ice?

Answer 1

Use this formula:

`c = Q/(m × ΔT)`

Explanation:

The specific heat formula is:

`c = Q/(m × ΔT)`

Where:

`c`: specific heat, in J/(kg.K)

`Q`: heat required for the temperature change, in J

`ΔT`: temperature change, in K

`m`: mass of the object, in kg

This may be difficult with ice due to its changing mass if temperature changes to above `0^o` C.

Here's an example problem and how you would go about solving it:
A piece of unknown metal weighs 348 g. When the metal piece absorbs 6.64 kJ of heat, its temperature increases from `22.4^oC` to `43.6^oC`. Determine the specific heat of this metal.

First, we should convert everything to the right units of measurement.

348 g of unknown metal x `(1 kg)/(1000 g)` = .348 kg

(Initial temperature) `22.4^oC` + 273.15 = 295.55 K

(Final temperature) `43.6^oC` + 273.15 = 316.75 K

`ΔT` = Final temperature - initial temperature = 316.75 - 295.55 = 21.2 K

6.64 kJ x `(1000 J)/( 1 kJ)` = 6640 J

Now, it's simply a matter of plugging the numbers in.

`c = (6640 J)/(.348 kg × 21.2^oC)`

`c = 900 J/(kg×C)`

Which can also be described as

`c = .9 J/(g×C)` if you want to express it in terms of grams.