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

Internal energy, denoted by the variables ΔE or ΔU, represents the total energy of a system, encompassing all forms of kinetic and potential energy. Understanding internal energy is crucial in thermodynamics, as it helps describe how energy is transferred within a system. The internal energy can be calculated using the equation:

\( \Delta E = q + w \)

In this equation, \( q \) represents the heat added to the system, while \( w \) denotes the work done on the system. This relationship highlights how internal energy changes in response to heat transfer and work interactions. By mastering this equation, students can better analyze energy changes in various thermodynamic processes, laying the groundwork for more advanced concepts in the field.

Internal Energy

The internal energy of a system is a crucial concept in thermodynamics, represented by the formula:

$$\Delta E = Q + W$$

In this equation, ΔE denotes the change in internal energy, which can be measured in joules (J) or kilojoules (kJ). The variable Q represents heat, also expressed in joules or kilojoules, while W signifies work done on or by the system.

To calculate work, we utilize the formula:

$$W = -P \Delta V$$

Here, P stands for pressure measured in atmospheres (atm), and ΔV represents the change in volume in liters (L). It is essential to note that 1 liter-atmosphere is equivalent to 101.325 joules, which serves as a conversion factor when work is expressed in liters times atmospheres.

Additionally, the concept of enthalpy, denoted as ΔH, is closely related to heat and work. Enthalpy represents the total heat content of a system and is particularly significant during chemical reactions. At constant pressure, enthalpy can be equated to heat:

$$\Delta H = Q$$

This relationship indicates that under constant pressure conditions, the change in enthalpy is equal to the heat absorbed or released by the system. It is vital to memorize these formulas, especially for quizzes and exams, as they form the foundation of understanding energy changes in thermodynamic processes.

Internal Energy Example 1

In thermodynamics, the internal energy of a system is a crucial concept that reflects the total energy contained within the system. When a reaction occurs at constant pressure, such as 20 atmospheres, and involves a volume change from 10 liters to 5 liters while releasing heat, we can calculate the change in internal energy using the formula:

ΔE = q + w

Here, ΔE represents the change in internal energy, q is the heat exchanged, and w is the work done on or by the system. In this scenario, the system releases 92.2 kilojoules of heat, which is expressed as:

q = -92.2 kJ

Since the system is doing work on the surroundings due to the volume compression, we need to calculate the work done. The work done can be calculated using the equation:

w = -PΔV

Where P is the pressure and ΔV is the change in volume. The change in volume is calculated as:

ΔV = V_final - V_initial = 5 L - 10 L = -5 L

Substituting the values, we find:

w = -20.0 atm × (-5 L) = 100 L·atm

To convert work from liters-atmospheres to kilojoules, we use the conversion factor:

1 L·atm = 101.325 J

Thus, we have:

w = 100 L·atm × 101.325 J/L·atm = 10132.5 J = 10.13 kJ

Now, substituting the values of q and w back into the internal energy equation gives:

ΔE = -92.2 kJ + 10.13 kJ = -82.07 kJ

This result indicates that the system has lost 82.07 kilojoules of energy during the process. Understanding this relationship between heat, work, and internal energy is fundamental in thermodynamics, as it helps predict how energy is transferred in chemical reactions and physical processes.

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.