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# Specific Heat

When summer hits, you might end up going to the beach to cool down. While the ocean waves may feel cool, the sand, unfortunately, is red-hot. If you aren't wearing shoes, it's possible to actually burn your feet!

But how can the water be so cold, but the sand be so hot? Well, that's because of their specific heat. Substances like sand have a low specific heat, so they heat up quickly. However, substances like liquid water have high specific heats, so they are much harder to heat up.

In this article, we will be learning all about specific heat: what it is, what it means, and how to calculate it.

• First, we will define heat capacity and specific heat.
• Then, we will talk about what units are commonly used for specific heat.
• Next, we will talk about the specific heat of water and why it is so important for life.
• Thereafter, we will look at a table of some common specific heats.
• Lastly, we will learn the formula for specific heat and work on some examples.

## Specific Heat Definition

We will begin by looking at the definition of specific heat.

Heat capacity is the amount of energy it takes to raise the temperature of a substance by 1 °C

Specific heat or specific heat capacity (Cp) is the heat capacity divided by the mass of the sample

Another way to think of specific heat is the energy it takes to raise 1 g of a substance by 1 °C. Basically, specific heat tells us how easily a substance's temperature can be raised. The larger the specific heat, the more energy it takes to heat it.

## Specific Heat Unit

Specific heat can have several units, one of the most common, which we will be using, is J/(g °C). When you are referencing specific heat tables, please pay attention to units!

There are other possible units, such as:

• J/(kg· K)

• cal/(g °C)

• J/(kg °C)

When we use units such as J/(kg·K), this follows a change in definition. In this case, specific heat refers to the energy required to raise 1 kg of a substance by 1 K (Kelvin).

## Specific Heat of Water

The specific heat of water is relatively high at 4.184 J/(g °C). This means that it takes about 4.2 Joules of energy to raise the temperature of just 1 gram of water by 1 °C.

Water's high specific heat is one of the reasons why it is so essential for life. Since its specific heat is high, then it is much more resistant to changes in temperature. Not only will it not heat quickly, it also won't release heat quickly either (i.e. cool down).

For example, our body wants to stay at about 37 °C, so if water's temperature could change easily, we would constantly either be over or underheated.

As another example, many animals rely on freshwater. If the water gets too hot, it could evaporate and many fish would be left without homes! Relatedly, salt water has a slightly lower specific heat of ~3.85 J/(g ºC), which is still relatively high. If salt water also had easily fluctuating temps, it would be devastating for marine life.

## Table of Specific Heats

While we sometimes determine specific heat experimentally, we also can reference tables for the specific heat of a given substance. Below is a table of some common specific heats:

Fig.1-Table of Specific Heats
Name of substanceSpecific heat (in J/ g °C)Name of substanceSpecific heat (in J/ g °C)
Water (s)2.06Aluminum (s)0.897
Water (g)1.87Carbon dioxide (g)0.839
Ethanol (l)2.44Glass (s)0.84
Copper (s)0.385Magnesium (s)1.02
Iron (s)0.449Tin (s)0.227

Specific heat is not only based on identity, but state of matter too. As you can see, water has a different specific heat when it is a solid, liquid, and gas. When you are referencing tables (or looking at example problems), make sure you pay attention to the state of matter.

## Specific Heat Formula

Now, let's take a look at the formula for specific heat. The specific heat formula is:

$$q=mC_p \Delta T$$

Where,

• q is the heat absorbed or released by the system

• m is the mass of the substance

• Cp is the specific heat of the substance

• ΔT is the change in temperature ($$\Delta T=T_{final}-T_{initial}$$)

This formula applies to systems that are either gaining or losing heat.

## Specific Heat Capacity Examples

Now that we have our formula, let's put it to use in some examples!

A 56 g sample of copper absorbs 112 J of heat, which increases its temperature by 5.2 °C. What is the specific heat of copper?

All we need to do here is solve for specific heat (Cp) using our formula:

$$q=mC_p \Delta T$$

$$C_p=\frac{q}{m*\Delta T}$$

$$C_p=\frac{112\,J}{56\,g*5.2 ^\circ C}$$

$$C_p=0.385\frac{J}{g ^\circ C}$$

We can check our work by looking at the table of specific heats (Fig.1)

As I mentioned earlier, we can also use this formula for when systems release heat (i.e are cooling).

A 112 g sample of ice cools from 33°C to 29°C. This process releases 922 J of heat. What is the specific heat of ice?

Since the ice is releasing heat, our q value will be negative, since this is a loss of energy/heat for the system.

$$q=mC_p \Delta T$$

$$C_p=\frac{q}{m*\Delta T}$$

$$C_p=\frac{-922\,J}{112\,g*(29 ^\circ C-33 ^\circ C)}$$

$$C_p=2.06\frac{J}{g^\circ C}$$

Like before, we can double-check our answer using Fig.1

We can also use specific heat to identify substances.

A 212 g sample of a silver metal absorbs 377 J of heat, which causes the temperature to rise by 4.6 °C, given the following table, what is the identity of the metal?

Fig.2-Possible metal identities and their specific heats
Name of MetalSpecific Heat (J/g°C)
Iron (s)0.449
Aluminum (s)0.897
Tin (s)0.227
Zinc (s)0.387

To find the identity of the metal, we need to solve for the specific heat and compare that to the table.

$$q=mC_p \Delta T$$

$$C_p=\frac{q}{m*\Delta T}$$

$$C_p=\frac{377\,J}{212\,g*4.6 ^\circ C}$$

$$C_p=0.387\frac{J}{g^\circ C}$$

Based on the table, the sample metal is Zinc.

## Calorimetry

You're probably wondering how we find these specific heats, one method is calorimetry.

Calorimetry is the process of measuring the exchange of heat between a system (such as a reaction) and a calibrated object called a calorimeter.

One of the common methods of calorimetry is coffee cup calorimetry. In this type of calorimetry, a styrofoam coffee cup is filled with a given amount of water at a given temperature. The substance whose specific heat we want to measure in, then place in that water with a thermometer.

The thermometer measures the change in heat of the water, which is used to then calculate the specific heat of the substance.

Below is what one of these calorimeters look like:

Fig.1-A coffee cup calorimeter

The wire is a stirrer used to keep the temperature uniform.

So, how does this work? Well, calorimetry works on this basic assumption: the heat lost by one species is gained by the other. Or, in other words, there is no net loss of heat:

$$-Q_{calorimeter}=Q_{substance}$$

OR

$$-mC_{water}\Delta T=mC_{substance}\Delta T$$

This method allows up to calculate the heat exchange (q) as well as the specific heat of whatever substance we choose. As mentioned in the definition, this also can be used to figure out how much heat a reaction releases or absorbs.

There is another type of calorimeter called a bomb calorimeter. These calorimeters are created to withstand high-pressure reactions, hence why it is called a "bomb".

Fig.2-A bomb calorimeter

The set-up of a bomb calorimeter is largely the same, except the material is much sturdier and the sample is held inside a container submerged in water.

## Specific Heat - Key takeaways

• Heat capacity is the amount of energy it takes to raise the temperature of a substance by 1 ºC
• Specific heat or specific heat capacity (Cp) is the heat capacity divided by the mass of the sample
• There are several possible units for specific heat, such as:
• J/g°C
• J/kg*K
• cal/g ºC
• J/kg ºC
• The specific heat formula is:

$$q=mC_p \Delta T$$

Where q is the heat absorbed or released by the system, m is the mass of the substance, Cp is the specific heat of the substance, and ΔT is the change in temperature ($$\Delta T=T_{final}-T_{initial}$$)

• Calorimetry is the process of measuring the exchange of heat between a system (such as a reaction) and a calibrated object called a calorimeter.

• Calorimetry is based on the assumption that: $$Q_{calorimeter}=-Q_{substance}$$

## References

Specific heat is the energy it takes for 1 g of a substance to be raised by 1 °C

Heat capacity is the energy it takes to raise the temperature of a substance by 1 °C.

4.184 J/ g°C is the specific heat of liquid water. For solid water (ice), it is 2.06 J/ g°C and for gaseous water (steam), it is 1.87 J/ g°C.

The standard units of specific heat are either J/g ºC, J/g*K, or J/kg*K.

The formula for specific heat is:

q=mCp(Tf-Ti)

Where q is the heat absorbed/released by the system, m is the mass of the substance, Cp is the specific heat, Tf is the final temperature, and Ti is the initial temperature

To get the specific heat, you divide the heat added/released by the system by the mass of the substance and the change in temperature.

## Final Specific Heat Quiz

Question

What is heat capacity?

Heat capacity is the amount of energy it takes to raise the temperature of a substance by 1 ºC

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Question

What is specific heat?

Specific heat or specific heat capacity (Cpis the heat capacity divided by the mass of the sample

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Question

What does specific heat tell us?

How easily a substance can heat up

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Question

Which of the following is NOT a possible unit for specific heat?

$$J/cal^\circ C$$

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Question

What is the specific heat of (liquid) water?

$$4.184 \frac{J}{g^\circ C}$$

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Question

Why is water's high specific heat so important?

Water's high specific heat is one of the reasons why it is so essential for life. Since its specific heat is high, then it is much more resistant to changes in temperature. Not only will it not heat quickly, it also won't release heat quickly either (i.e. cool down).

Show question

Question

True or False: Specific heat is dependent on state of matter

True

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Question

What is the formula for specific heat?

$$q=mC_p\Delta T$$

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Question

True or False: The specific heat equation only applies to substances being heated

False

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Question

True or False: Specific heat also determines how easily a substance will cool

True

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Question

What is calorimetry?

Calorimetry is the process of measuring the exchange of heat between a system (such as a reaction) and a calibrated object called a calorimeter.

Show question

Question

Calorimetry is based on what assumption?

$$-Q_{calorimeter}=Q_{substance}$$

Show question

Question

A 316 g sample of a silver metal absorbs 992 J of heat to raise its temperature by 3.5 °C, given the following specific heats, what is the identity of the metal?

• Iron (0.449 J/g°C)
• Aluminum (0.897 J/g°C)
• Zinc (0.387 J/g°C)
• Tin (0.227 J/g°C)

Aluminum

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Question

A 47 g sample of copper cools from 25°C to 20°C, releasing 90.5 J of heat. What is the specific heat of copper?

0.385 J/g°C

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Question

A 58 g sample of glass is heated by 175 J, causing a temperature change of 3.6°C. What is the specific heat of the glass?

0.84 J/g°C

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