Specific heat capacity

Specific heat capacity, also called specific heat or thermal capacity, is defined as the amount of heat needed to raise the temperature of a substance by 1 degree.

Just like the definition might suggest, the amount of heat needed will vary and depend on the substance.

For example, it takes a pot of water on the stove about 15 minutes to go from room temperature to its boiling point.

However, if you put an equal mass of silver on the same flame, it will take less than a minute to rise to the same temperature.

We say that silver has a lower specific heat capacity than water since silver will get hot much quicker than water.

A substance that has a high specific heat will remain hot for a longer period of time while a substance with a low specific heat will remain hot for a shorter period of time.

Many people use aluminum foil to cover their food while the food is cooking in the oven.

After you remove the food from the oven, did you notice that you can peel off the aluminum foil with your bare fingers?

The reason for this is because aluminum foil has a low specific heat.

It gets hot very fast in the oven. However, as soon as it comes out of the oven, it will cool down very fast.

You will get a different result if you put an iron tray in the oven.

You will have to wait a long time before you can touch it. Again, it is because it takes longer to get hot and longer to cool down as well.

Recall that 1 calorie is the amount of heat required to raise the temperature of 1 gram of water by 1 degree celsius. 

We can say that the specific heat of water is 1 cal/g°C

As you can see, the unit of specific heat is cal/g°C (calories per gram °C)

The specific heat of a substance does not change. The amount of heat needed then will depend on the mass of the substance and the temperature.

What is the amount of heat needed for 4 grams of water?

Since 1 gram requires 1 calory, does it make sense to say that 4 grams will require 4 calories?

Mathematically, this can be expressed as

4 g × 1 cal/g × 1 °C = 4 calories.

Notice that multiplication is the best way to express this relationship between specific heat, mass, and temperature.

What is the amount of heat needed to raise 4 grams of water by 3 degree Celsius?

1 degree Celsius requires 4 calories, so 3 degrees Celsius will require 12 calories.

Mathematically, this can be expressed as

4 g × 1 cal/g × 3 °C = 12 calories.

Specific heat capacity formula

The following specific heat capacity formula can be used to measure the quantity of heat or the amount of heat tranferred.

Q = mcΔT

What is the number of calories needed to raise the temperature of 3 liter of water by 20 degrees Cesius?

1 liter of water is equal to 1000 grams, so 3 liters of water will equal to 3000 grams. Now, just use the formula

Q = mcΔT

Q = 3000 g × 1 cal/g × 20

Q = 60,000 calories.

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