Heat Capacity - Online Tutor, Practice Problems & Exam Prep

Heat capacity, denoted by the capital letter C, is the amount of heat required to raise the temperature of a given quantity of a substance. It's directly proportional to the temperature change, implying that more heat results in a greater temperature increase. Specific heat capacity, represented by lowercase c, refers to the heat needed to raise the temperature of 1 gram of a substance by 1 degree Celsius or Kelvin. Molar heat capacity, also denoted by capital C, is similar but relates to one mole of a substance. The equations for molar heat capacity and specific heat capacity are:

$C=\frac{Q}{n∆T}$

and

$c=\frac{Q}{m∆T}$

where Q is heat in joules, n is the number of moles, m is the mass in grams, and ΔT is the temperature change. By rearranging, the heat (Q) absorbed or released can be calculated with the formula:

$Q=mc∆T$

a crucial concept for understanding energy changes in chemical reactions.

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 being directly proportional to ΔT. So 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. Now it can be looked at also in terms of specific heat capacity and molar heat capacity.

With specific heat capacity, we use lower case c, and it is the amount of heat required to change the temperature of 1g of a substance by 1�. That degree can be either in Kelvin or degrees Celsius. Here, molar heat capacity is just like heat capacity in terms of it being 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� either in Kelvin or degrees Celsius.

OK, 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 QN⁢ΔT. So capital C equals our molar heat capacity in Joules over 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, temperature should match it. OK, so if this happened to be in Kelvin, then temperature should be in Kelvin, and then N is equal to our moles. With our specific heat capacity, it uses lower case c, it equals Qm⁢ΔT. Here, lowercase c is our specific heat capacity in joules over grams times degrees Celsius or Kelvin.

Q again is heat, 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 lower case 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 one 5.7g silver raised its temperature by 17.2�C, when it absorbs 6845.5 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 that's a positive cue. So that's +6845.5 Joules. Next we need moles, and we already have the change in temperature. They say that the temperature was risen by 17.2�C, so that's already our change in temperature.

We need moles. We have here 15.7 grams of silver, which is AG. We have to change that to molds. SO1 mole of silver weighs one O 7.87g according to the periodic table, so that comes out to be .145548 moles of silver. Take those moles and plug it in.

So when we do that, that's going to give me my molar heat capacity AS27 34.45 Joules over moles times degrees Celsius. If we look at our values, this has three sig figs and this has three sig figs. So I could change this to 2.73 * 10 to the three joules over moles times degrees Celsius. So that would be the molar heat capacity for silver under these conditions.

C = Q n ⋅ ∆ T

Heat Capacity

Now by rearranging the specific key 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⁢∆T 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, so use that to help you remember it. So Q=MCAT is our new formula to help us determine and relate the specific key capacity to the amount of heat absorbed or released in a chemical reaction.

Heat Capacity Example 3

Here it says how much heat in kilojoules is released when 120 grams of water goes from 90�C to 45�C. The specific heat capacity of water is given as 4.184 joules over grams times degrees Celsius. So we need to determine the heat, which is Q. They're giving us here the mass of the water, which is M. We have our change in temperature here and we have our specific heat capacity is lower case C, so Q=MCΔT.

Plug in the grams of water given to us. Plug in these specific heat capacity that's given to us. And remember the units for the specific heat capacity dictate the units for temperature. Since this is in Celsius, it's good to have our temperatures in Celsius as well. ΔT is final minus initial, So when we do all that Celsius cancel out, grams cancel out and we'll have Joules of heat involved.

When we plug that in, we're going to get here -22593.6 joules. But here we want the answer in kilojoules, so one KJ is equal to 10^3 joules. So here, joules cancel out and we'll have kilojoules at the end. So that comes out to -22.5936 kilojoules.

Here. This has four sig figs, one sig fig, 2 sig figs specific incapacity. We could use it since it's given to us as a value, but we don't have to here. We could just go with one sig fig, but I feel like that's too much rounding, so let's just go with two sig figs based on 45, so it's gonna be -23. Roughly kilojoules of heat are released, so here using Q=MCΔT, we're able to isolate the heat that's involved in the releasing by the water molecule going from 90�C to 45�C.

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?

• 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 heat capacity?

Heat capacity is a physical property of a substance that measures the amount of heat energy required to raise the temperature of a given amount of the substance by one degree Celsius (or one Kelvin). It is an extensive property, meaning it depends on the amount of the substance present. The heat capacity of a system can be measured at constant volume ($C_v$), where the volume is held fixed, or at constant pressure ($C_p$), where the pressure remains constant during the heating process.

The heat capacity is often reported in units of joules per degree Celsius (J/°C) or joules per kelvin (J/K). For a given substance, the heat capacity can vary depending on its temperature, pressure, and physical state (solid, liquid, or gas). The concept of heat capacity is critical in various fields, including chemistry, physics, engineering, and environmental science, as it helps predict how substances absorb and transfer heat under different conditions.

What is specific heat capacity?

Specific heat capacity is a physical property of a material that measures the amount of heat energy required to raise the temperature of one unit of mass of the substance by one degree Celsius (or one Kelvin). It's usually expressed in units of joules per gram per degree Celsius (J/g°C) or joules per kilogram per Kelvin (J/kg·K). Different substances have different specific heat capacities, which is why some materials heat up or cool down more quickly than others.

For example, water has a high specific heat capacity, which means it can absorb a lot of heat without a significant rise in temperature. This property is crucial in various applications, such as climate regulation and thermal energy storage. In contrast, metals typically have lower specific heat capacities, so they tend to heat up and cool down more rapidly, making them useful in applications like cooking utensils. Understanding specific heat capacity is essential in fields like thermodynamics, material science, and engineering.

How do you calculate specific heat capacity?

To calculate the specific heat capacity (c) of a substance, you need to know the amount of heat energy (Q) absorbed or released by the substance, the mass (m) of the substance, and the change in temperature (ΔT) the substance undergoes. The specific heat capacity is the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin).

The formula to calculate specific heat capacity is:

$c=\frac{Q}{m\cdot \mathrm{\Delta T}}$

Where:

• c is the specific heat capacity (usually in Joules per gram per degree Celsius, J/g°C)
• Q is the heat energy added or removed (in Joules, J)
• m is the mass of the substance (in grams, g)
• ΔT is the change in temperature (in degrees Celsius, °C or Kelvin, K)

Make sure to use consistent units when performing the calculation. If the substance is heating up, ΔT will be positive; if it's cooling down, ΔT will be negative. Remember, the specific heat capacity is a characteristic property of a material and does not change with the amount of the substance.

How do you calculate heat capacity?

Heat capacity, which is the amount of heat energy required to raise the temperature of a substance by one degree Celsius, can be calculated using the formula:

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

where:

• C is the heat capacity,
• q is the amount of heat added (in joules or calories), and
• ΔT is the change in temperature (in degrees Celsius or Kelvin).

For example, if you add 500 joules of heat to a substance and its temperature increases by 5 degrees Celsius, the heat capacity would be:

$C=\frac{500}{5}=100\text{J/°C}$

This means the substance has a heat capacity of 100 joules per degree Celsius. If you're calculating the specific heat capacity, which is the heat capacity per unit mass, you would also divide by the mass of the substance. The formula for specific heat capacity (c) is:

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

where m is the mass of the substance. For instance, if the mass of the substance is 2 kilograms, the specific heat capacity would be:

$c=\frac{500}{2\cdot 5}=50\text{J/(kg°C)}$

How do you calculate molar heat capacity?

Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius (or one Kelvin). To calculate it, you need to conduct an experiment where you add a known amount of heat to a known number of moles of the substance and measure the temperature change.

Here's the formula to calculate molar heat capacity (C):

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

Where:

• C is the molar heat capacity (usually in J/mol·K)
• q is the amount of heat added (in joules, J)
• n is the number of moles of the substance
• ΔT is the change in temperature (in Kelvin, K or degrees Celsius, °C)

Remember, when you perform the experiment, you must ensure that the heat is transferred only to the substance of interest and that all of it is used to change the temperature of the substance. This is often done in a calorimeter, which is designed to minimize heat loss to the surroundings.