Internal Energy: Videos & Practice Problems

Internal energy ($\mathrm{\Delta E}$ or $\mathrm{\Delta U}$) encompasses the total kinetic and potential energy within a system. It is calculated using the formula:

$\mathrm{\Delta E}=Q+W$

where $Q$ represents heat and $W$ stands for work performed by or on the system. Work itself can be further defined by the equation:

$W=-P\Delta V$

with $P$ indicating pressure in atmospheres and $V$ representing volume in liters. To convert work from liters-atmospheres to joules, the factor of 101.325 joules per liter-atmosphere is used. Additionally, enthalpy ($\mathrm{\Delta H}$), which measures heat change during a reaction at constant pressure, is equivalent to $Q$ under these conditions. Understanding these relationships and conversions is crucial for analyzing energy changes in chemical processes.

Internal Energy

So internal energy uses the variable of Delta E, which is the more common variable, or delta U which is the less common variable. But you might see either 1. So be mindful that both mean internal energy.

Here we're going to say it represents the total energy from all forms of kinetic and potential energy of a system. Now we're going to say internal energy can be calculated as ΔE=Q+W. So this is our understanding when it comes to the internal energy of a system.

Now that we have this basic equation, click on to the next video and let's go a little bit deeper in terms of it.

Internal Energy

Now with the internal energy of a system, we have the internal energy formula. We're going to say this formula is used when we have the heat and work of a system. We know that ΔE=Q+W. ΔE is our internal energy. It can be in either joules or kilojoules. Q represents our heat. It can also be in joules or kilojoules. And then W equals work.

Now with work we have an additional formula. Here the work formula is used when we have the pressure and volume of a system. Here work equals negative times delta VS. We're going to say here P equals pressure in atmospheres, V equals volume in liters, and then we're going to say liters times atmospheres is equivalent to 101.325 Joules. Now this is important because if work is given in liters times atmospheres, then we use this conversion factor here to change it into joules.

And we're going to say here, connected to this idea of heat and work is another term, enthalpy, which uses the variable of ΔH. We're going to say it represents the amount of heat released or absorbed during chemical reaction. It should sound kind of familiar to you. We're going to say here that at constant pressure, enthalpy and heat can be treated as the same variable. So at constant pressure, we're going to say here that enthalpy, which is ΔH, is equal to heat, which is Q.

So keep these formulas in mind. Because remember, if it has a purple box around it, that means you're responsible for memorizing it for any upcoming quizzes or exams. So remember internal energy equals Q+W and work equals negative pressure times change in volume.

Internal Energy Example 1

Here we're told what is the internal energy of the system if the reaction is done at a constant pressure of 20 atmospheres and the volume compresses to 10 liters to 5 liters while releasing 92.2 kilojoules of heat. All right, so internal energy is ΔE and it equals Q + W. They tell us that we're releasing 92.2 kilojoules of heat. Remember, if you're releasing heat, it has a negative sign, so it's -92.2 kilojoules.

Since heat is in kilojoules, work needs to be in kilojoules. Remember, work equals negative. Pressure times change in volume, so -20.0 atmospheres times change in volume, which is final minus initial, so 5 liters, -10 liters. So here when we do that, that's going to give me a positive 100 liters times atmospheres, and here we need kilojoules for work, so we're going to have to do some converting.

So we have 100 liters times atmospheres. Remember one liter times at one liter times atmospheres equals one O 1.325 Joules. And then remember one KJ is equal to 10 to the three joules. So that's going to give me one 0.13 25 joules. Here we'll just round to 10.13 Joules. I'll killjoules. Now we're going to take that and plug it in O. Here I'm going to take this is my work and plug it into here.

So now we're going to plug this into our calculators, and when we do, that's going to give us the internal energy of our system. So let me rewrite it down here. So we're going to say ΔE = Q + W, so it equals -92.2 plus 10.13. So when we do that, we're going to get our answer as -82.07 kilojoules. This tells me how much energy my system has lost through this process. So just remember internal energy equals Q + W.

An unknown gas expands in a container increasing the volume from 4.3 L to 8.2 L at a constant pressure of 931 mmHg. Calculate the internal energy of the system if the system absorbs 2.3 kJ of energy. 

• A. 2.3 kJ
• B. 1.8 kJ
• C. 1.2 kJ
• D. 2.8 kJ

Answer: (B)

A gas reaction is allowed to take place in a canister while submerged in water at a temperature of 25^oC. The gas expands and does P-V work on the surroundings equal to 385 J. At the same time, the temperature of the water decreases to 20^oC as the energy in the gas reaction reaches 364 J. What is the change in energy of the system? 

• A. 21 J
• B. -32 J
• C. -21 J
• D. 134 J

Answer: (C)

Here’s what students ask on this topic:

What is internal energy?

Internal energy is a concept in thermodynamics representing the total energy contained within a system. It encompasses all forms of energy present within a system, which includes the kinetic energy of particles moving and vibrating, as well as the potential energy resulting from the forces that act within or between these particles. In a more detailed sense, this means considering the translational, rotational, vibrational kinetic energies of molecules, as well as any electronic energy levels, and the potential energy of molecular bonds and intermolecular forces.

Internal energy is a state function, meaning it depends only on the current state of the system and not on how the system reached that state. It's an extensive property, which implies that the internal energy of a system scales with the amount of substance in the system. Changes in a system's internal energy can be brought about through heat transfer, work done by or on the system, and matter transfer. In the context of the first law of thermodynamics, the change in internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings.

How do you calculate the change in internal energy?

To calculate the change in internal energy of a system, you can use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W):

$∆U=Q-W$

Here's what each term represents:

• ΔU (Change in Internal Energy): This is what you're solving for. It's the difference between the final and initial internal energy of the system.
• Q (Heat): This is the amount of heat transferred into or out of the system. If heat is added to the system, Q is positive; if heat is lost from the system, Q is negative.
• W (Work): This is the work done by the system. If the system does work on its surroundings (like when a gas expands), W is positive. If work is done on the system (like when a gas is compressed), W is negative.

Remember, the sign conventions for Q and W can vary depending on the context, but the one provided here is commonly used in physics and chemistry. To find the change in internal energy, you'll need to know or measure the heat and work for the process in question.

What is enthalpy?

Enthalpy is a concept in thermodynamics that represents the total heat content of a system. It's a measure of the energy in a thermodynamic system that is available for doing mechanical work. Enthalpy is denoted by the symbol 'H' and is typically expressed in units of joules (J) in the International System of Units (SI).

You can think of enthalpy as a combination of internal energy (the energy required to create a system) and the work needed to make space for it (the pressure-volume work). It's important because it helps us understand how much heat is absorbed or released during a chemical reaction at constant pressure.

When a reaction occurs at constant pressure and the only work done is due to expansion or contraction, the change in enthalpy (ΔH) equals the heat (q) absorbed or released by the system. This is often what you're calculating in chemistry when you're looking at heat changes during reactions, and it's especially useful for understanding exothermic and endothermic processes.

How do you calculate enthalpy change?

Enthalpy change, denoted as ΔH, is the measure of heat change in a system at constant pressure. To calculate enthalpy change, you can use the following methods:

1. Using Heat Capacity and Temperature Change: If you know the specific heat capacity of the substance (c) and the mass of the substance (m), you can calculate the enthalpy change when the temperature changes by ΔT using the formula: $\mathrm{\Delta H}=m*c*\mathrm{\Delta T}$
2. Hess's Law: If a reaction can be expressed as the sum of a series of steps, then the enthalpy change for the overall reaction is the sum of the enthalpy changes for each individual step.
3. Standard Enthalpies of Formation: The enthalpy change for a reaction can be calculated using the standard enthalpies of formation (ΔH_f°) of the reactants and products: $\mathrm{\Delta H}=\Sigma \left(\mathrm{\Delta H}{f}_{°}\text{of products}\right)-\Sigma \left(\mathrm{\Delta H}{f}_{°}\text{of reactants}\right)$
4. Bond Energies: If you know the bond energies, the enthalpy change can be estimated by subtracting the total bond energy of the bonds formed in the products from the total bond energy of the bonds broken in the reactants.

Remember to keep track of the units.