# How do you determine the specific heat of ice?

Jan 9, 2017

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 ${22.4}^{o} C$ to ${43.6}^{o} C$. Determine the specific heat of this metal.

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

348 g of unknown metal x $\frac{1 k g}{1000 g}$ = .348 kg

(Initial temperature) ${22.4}^{o} C$ + 273.15 = 295.55 K

(Final temperature) ${43.6}^{o} C$ + 273.15 = 316.75 K

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

6.64 kJ x $\frac{1000 J}{1 k J}$ = 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.