# How to determine specific heat capacity

1. Jun 6, 2014

### Nerdydude101

I have been looking for specific heat capacities of certain materials such as steel but i can never find a solid answer, so i figured i would test it myself, how would one test specific heat capacities?

2. Jun 6, 2014

### Andrew Mason

Steel is not an element. It contains iron and carbon and probably lots of other elements. So its heat capacity will depend to some extent on what it contains.

Heat capacity is: heat flow/temperature change = Q/ΔT. The difficulty is in measuring heat flow. The way this is usually done is by measuring the change in temperature of some other substance, such as water for which we know the heat capacity: eg. measure the temperature and mass of the steel and immerse it in a known mass of water at 0°C in a calorimeter. When equilibrium is reached, measure the temperature, work out the temperature change of the system to find the heat flow.

AM

3. Jun 6, 2014

### SteamKing

Staff Emeritus
4. Jun 6, 2014

### CWatters

Heat up the steel and drop it into a container of water. If you know the temperatures before and after you can work out how much heat energy the steel contained and calculate the specific heat capacity. However this relies on an assumption that no heat is lost to the surroundings so the experiment has to be done with some care to get an accurate result. Variations on this theme are common physics exam questions.

5. Jun 6, 2014

### dauto

You will need a calorimeter.

6. Jun 6, 2014

### AlephZero

There are literally about 10,000 different grades of steel with different chemical compositions, and different thermal properties. The specific heat capacity also varies with temperature.

See here (near the bottom of the page) for typical values for low alloy steel, plus several grades of nickel steels and stainless steels. http://www.kayelaby.npl.co.uk/general_physics/2_3/2_3_6.html

7. Jun 6, 2014

### Impulse

Is the elementary notion of a constant "c" for each material a simplification? In reality does this "constant" vary with the material's temperature?

Is that simplification of specific heat into a "constant" when in reality more factors are involved the same simplification made for resistance, in which elementary physics assumes that for each material a constant resistance exists irrespective of the amount of current traveling through the material?

8. Jun 7, 2014

### CWatters

Also varies with state?

Water at 100 °C (steam) gas 2.080
Water at 25 °C liquid 4.1813
Water at 100 °C liquid 4.1813
Water at −10 °C (ice)[26] solid 2.11

From http://en.wikipedia.org/wiki/Heat_capacity

9. Jun 7, 2014

### Impulse

Ahh, cool!

My physics class (HS intro level) analyzed heat interaction as if specific heat was constant for all substances in all states at all temperatures. That intuitively sounds wrong.

What determines specific heat at the atomic level? Is it very complex?

10. Jun 7, 2014

### Andrew Mason

It is not always wrong. In fact, it is correct for some substances for most temperatures, such as Helium (an ideal monatomic gas).

Temperature is a measure of the average translational kinetic energy of the molecules. Heat flow is energy flow that causes the kinetic energy of the molecules to change. So in a simple case of an ideal monatomic gas such as He, the ratio of heat flow to temperature change is perfectly linear for nearly all temperatures.

The problem is that heat capacity is complicated if there are diatomic or polyatomic molecules. These introduce quantum effects.

With diatomic and polyatomic molecules kinetic energy of molecules can be in different modes, such as rotational and vibrational KE as well as translational KE. When heat is transferred to a substance some of these modes may be excited and some not and this will affect heat capacity.

Also, heat capacity is complicated by inter-molecular forces (eg. water).

To fully grasp heat capacity you will have to study kinetic theory. Here is a good starting point.

AM