Heat Capacity: Study with Video Lessons, Practice Problems & Examples

Heat capacity measures the heat required to change a substance's temperature, with specific heat capacity (c) defined as the heat needed to raise 1 gram by 1°C, and molar heat capacity (C) for 1 mole. The equations are q=mcΔT for specific heat and C=q⁄nΔT for molar heat. Understanding these concepts is crucial for thermochemistry and calorimetry applications.

Heat Capacity

So when we talk about heat capacity, we're talking about the application of heat to a substance. We're going to say as we heat an object, its temperature increases because heat is directly proportional to its temperature change. The more heat I apply to something the greater the temperature change will be. So, here to illustrate that, we say that q∝ΔT. Just remember, that is the relationship between heat and temperature.

Heat Capacity Example 1

Here it says if the temperature of a water bath goes from 25 Kelvin to 50 Kelvin, what can be said about the amount of heat? So remember we said that heat, which is q, is directly proportional to change in temperature. Here our temperature is going from 25 Kelvin to 50 Kelvin, so it is being doubled in terms of Kelvin. And since they're directly proportional, what happens to one happens to the other. With our temperature doubling, that would mean that my heat would also have to double. This means that option a would be our correct answer.

Heat Capacity

Now, heat capacity, which uses capital C, is the amount of heat required to change the temperature of a weighted substance. The more heat that's applied to a substance, the greater its temperature change. It can also be looked at in terms of specific heat capacity and molar heat capacity. With specific heat capacity, we use lowercase c, and it is the amount of heat required to change the temperature of 1 gram of a substance by 1 degree. That degree can be either in Kelvin or degrees Celsius. Here, molar heat capacity is just like heat capacity in terms that it uses a capital C. But here, with molar heat capacity, it's the amount of heat required to change the temperature of 1 mole of a substance by 1 degree, either in Kelvin or degrees Celsius. Okay? So think of molar heat capacity as being a little bit more focused in terms of the way we look at heat capacity, in terms of 1 mole of a substance.

Now, we're going to say here that when it comes to molar heat capacity, which is capital C, it equals C=qn⋅ΔT. So capital C equals our molar heat capacity in joules per moles times degrees Celsius or in Kelvin. Q represents heat, t equals temperature in degrees Celsius. But what we need to realize here is that whatever the units that the molar heat capacity uses for temperature, the temperature should match it. K? So if this happened to be in Kelvin then the temperature should be in Kelvin. And then n is equal to our moles. With our specific heat capacity, it uses lowercase c, it equals c=qm⋅ΔT. Here lowercase c is our specific heat capacity in joules per grams times degrees Celsius or Kelvin. Q again is heat. The temperature again can be in Celsius or in Kelvin. To determine which one to use, you look at the units for your specific heat capacity and make sure they match. And then lowercase m here is just grams of our substance. So just remember the difference between molar heat capacity and specific heat capacity.

Heat Capacity Example 2

Here the example says, if 15.7 grams of silver raises its temperature by 17.2 degrees Celsius when it absorbs 6,845.5 joules, what is its molar heat capacity? So molar heat capacity uses capital C. It's equal to heat, which is Q divided by moles n times change in temperature. In the question, it says that we're absorbing this much energy. That means that it's a positive Q. So that's positive 6,845.5 joules. Next, we need moles, and we already have the change in temperature. They said that the temperature was risen by 17.2 degrees Celsius. So that's already our change in temperature. We need moles, we have here 15.7 grams of silver which is a g. We have to change that to moles, so one mole of silver weighs 107.87 grams according to the periodic table. So that comes out to be 0.145548 moles of silver. Take those moles and plug them in. So when we do that it's going to give me my molar heat capacity as 2734.45moles× degrees Celsius joules. If we look at our values, this has 3 significant figures, and this has 3 significant figures, so I could change this to 2.73×103 joules over moles times degrees Celsius. So that would be the molar heat capacity for silver under these conditions.

Heat Capacity

Now by rearranging the specific heat capacity given above, we can solve for the amount of heat released or absorbed. Here our new specific heat capacity formula becomes q = m ∙ c ∙ Δt. For all of you pre-med track students, we usually say that this is equal to q = mcat, and we know that the MCAT is an important exam before you matriculate into medical school. Use that to help you remember it. So q = mcat is our new formula to help us determine and relate the specific heat capacity to the amount of heat absorbed or released in a chemical reaction.

A sample of copper absorbs 3.53 kJ of heat, which increases the temperature by 25 ºC, determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J / g  ºC.

• A. 0.73 kg
• B. 0.35 kg
• C. 0.37 kg
• D. 0.53 kg

Based on their given specific heat capacities which substance would show the greatest temperature change upon absorbing 25.0 J of heat? 

• A. 250.0 g Al
• B. 250.0 g Cu
• C. 250.0 g ethanol
• D. 250.0 g wood

50.00 g of heated metal ore is placed into an insulated beaker containing 822.5 g of water. Once the metal heats up the final temperature of the water is 32.08 ºC. If the metal gains 14.55 kJ of energy, what is the initial temperature of the water? The specific heat capacity of copper is 4.184 J / g  ºC.

• A. 23.86 °C
• B. 32.86 °C
• C. 63.08 °C
• D. 36.31 °C

Here’s what students ask on this topic:

What is the difference between specific heat capacity and molar heat capacity?

Specific heat capacity (c) is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C or 1 K. It is expressed in units of J/g·°C or J/g·K. Molar heat capacity (C), on the other hand, is the amount of heat required to raise the temperature of 1 mole of a substance by 1°C or 1 K. It is expressed in units of J/mol·°C or J/mol·K. The key difference lies in the amount of substance being considered: specific heat capacity deals with mass (grams), while molar heat capacity deals with the number of moles.

How do you calculate the amount of heat absorbed or released using specific heat capacity?

To calculate the amount of heat (q) absorbed or released using specific heat capacity (c), you can use the formula:

$q=mc\mathrm{\Delta T}$

Here, $m$ is the mass of the substance in grams, $c$ is the specific heat capacity, and $\mathrm{\Delta T}$ is the change in temperature in °C or K. This formula helps determine the heat exchanged during a temperature change.

Why is heat capacity important in thermochemistry?

Heat capacity is crucial in thermochemistry because it helps quantify the amount of heat energy required to change the temperature of a substance. This information is essential for understanding and predicting the energy changes in chemical reactions and physical processes. By knowing the heat capacity, scientists can calculate the heat absorbed or released during reactions, which is vital for designing experiments, industrial processes, and understanding natural phenomena.

What units are used for specific heat capacity and molar heat capacity?

Specific heat capacity (c) is typically measured in units of J/g·°C or J/g·K, which represent the amount of heat required to raise the temperature of 1 gram of a substance by 1°C or 1 K. Molar heat capacity (C) is measured in units of J/mol·°C or J/mol·K, indicating the amount of heat needed to raise the temperature of 1 mole of a substance by 1°C or 1 K. The choice of units depends on whether the measurement is based on mass or moles.

How does the formula for molar heat capacity differ from that of specific heat capacity?

The formula for molar heat capacity (C) is:

$C=\frac{q}{n\mathrm{\Delta T}}$

Here, $q$ is the heat absorbed or released, $n$ is the number of moles, and $\mathrm{\Delta T}$ is the change in temperature. For specific heat capacity (c), the formula is:

$c=\frac{q}{m\mathrm{\Delta T}}$

Here, $m$ is the mass in grams. The main difference is that molar heat capacity uses moles, while specific heat capacity uses mass.