How to Find Internal Energy:3 Important Factors to Consider!

How to Find Internal Energy

Internal energy is a fundamental concept in physics and thermodynamics that plays a crucial role in understanding the behavior of various systems. In this blog post, we will explore the definition and importance of internal energy, how to calculate it in different scenarios, and its significance in specific substances. So, let’s dive right in!

Definition and Importance of Internal Energy

Internal energy refers to the total energy contained within a system, including both the kinetic and potential energy of its particles. It represents the microscopic energy associated with the random motions and interactions of particles at the molecular level. The internal energy of a system depends on its temperature, pressure, and composition.

Understanding internal energy is essential because it helps us analyze and predict the behavior of substances and systems. It allows us to explain phenomena such as heat transfer, changes in states of matter, and the behavior of gases. By accurately calculating internal energy, we can gain insights into the thermodynamic properties and stability of a system.

The Role of Internal Energy in Physics and Thermodynamics

Internal energy is a fundamental concept in physics and thermodynamics. It serves as a bridge between macroscopic and microscopic properties of matter. By studying internal energy, we can understand the relationship between heat, work, and energy.

Internal energy is closely related to other thermodynamic properties such as temperature, pressure, and volume. Changes in internal energy can be influenced by factors like heat transfer, work done on or by the system, and changes in the system’s surroundings. By analyzing these relationships, we can explain and predict the behavior of substances and systems under different conditions.

Finding Internal Energy in Different Scenarios

How to Calculate Internal Energy Given Pressure

One way to calculate internal energy is by using the equation:

$\Delta U = q - w$

where $\Delta U$ represents the change in internal energy, $q$ is the heat transferred to the system, and $w$ is the work done by the system. This equation is based on the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

Determining Internal Energy with Kinetic Energy

In certain scenarios, we can calculate internal energy by considering the kinetic energy of the particles within the system. For example, in an ideal gas, the internal energy is directly related to the average kinetic energy of its particles. The equation for internal energy in an ideal gas is:

$U = \frac{3}{2} nRT$

where $U$ is the internal energy, $n$ is the number of moles of gas, $R$ is the ideal gas constant, and $T$ is the temperature in Kelvin.

Measuring Internal Energy with Pressure and Volume

For certain systems, we can determine the internal energy by using the equation:

$\Delta U = q + w = q - P \Delta V$

where $\Delta U$ is the change in internal energy, $q$ is the heat transferred to the system, $w$ is the work done by the system, $P$ is the pressure, and $\Delta V$ is the change in volume. This equation takes into account the work done by the system against external pressure.

Worked Out Example: Finding Internal Energy of a System

Let’s consider an example to illustrate how to find the internal energy of a system. Suppose we have a gas confined in a cylinder with a movable piston. The gas is initially at a pressure of 2 atmospheres and a volume of 3 liters. If the gas expands against a constant external pressure of 1 atmosphere to a final volume of 6 liters, and 1000 Joules of heat is added to the system, we can calculate the change in internal energy.

Using the equation $\Delta U = q - P \Delta V$ , we can substitute the values:

$\Delta U = 1000J - (1 atm)(6L-3L)$

Simplifying, we have:

$\Delta U = 1000J - 3 atm \cdot L$

Therefore, the change in internal energy is $997 J$ .

Internal Energy in Specific Substances

Finding the Internal Energy of Steam

In the case of steam, the internal energy can be determined using steam tables. Steam tables provide information about the specific internal energy of steam at different temperatures and pressures.

Calculating the Internal Energy of Combustion

The internal energy of combustion can be calculated by considering the energy released during the combustion reaction. This energy is typically expressed as the heat of combustion, which represents the change in internal energy when one mole of a substance combusts completely.

Determining the Internal Energy of Helium

The internal energy of helium can be calculated based on its atomic structure and the energy levels of its electrons. By considering the energy associated with electron transitions, we can determine the internal energy of helium.

Measuring the Internal Energy of a Gas

For a gas, the internal energy depends on its temperature and the specific heat capacity. The equation for the internal energy of a gas is:

$U = nC_vT$

where $U$ is the internal energy, $n$ is the number of moles of gas, $C_v$ is the molar specific heat at constant volume, and $T$ is the temperature in Kelvin.

Worked Out Example: Using a Steam Table to Find Internal Energy

Let’s consider an example of how to use a steam table to find the internal energy of steam. Suppose we have steam at a temperature of 150°C and a pressure of 2 atmospheres. We can look up the specific internal energy value for these conditions in a steam table, which might be $2500 J/g$ .

Therefore, the internal energy of the steam is $2500 J/g$ .

Changes in Internal Energy

Understanding Internal Energy Change

Internal energy change refers to the difference in internal energy between two states or conditions of a system. It can occur due to heat transfer, work done on or by the system, or changes in the system’s surroundings.

Factors Affecting Internal Energy Change

Several factors can affect the change in internal energy of a system, including temperature effects, pressure effects, heat transfer, and work done. For example, increasing the temperature of a substance generally increases its internal energy, while compressing a gas can increase its internal energy.

Worked Out Example: Calculating Internal Energy Change

Consider the example of a gas that expands against a constant external pressure. If the gas does 500 Joules of work and releases 300 Joules of heat, we can calculate the change in internal energy using the equation $\Delta U = q - w$ :

$\Delta U = 300J - 500J$

Therefore, the change in internal energy is $-200 J$ .

Recap of Key Points on Finding Internal Energy

Internal energy refers to the total energy contained within a system and plays a crucial role in understanding the behavior of substances and systems.
Internal energy can be calculated using various equations, such as the first law of thermodynamics and specific equations for different scenarios.
Steam tables can be used to find the internal energy of steam, while other substances may require different approaches based on their properties and characteristics.
Changes in internal energy can occur due to factors like heat transfer, work done, and changes in temperature or pressure.

Accurately calculating internal energy is vital in various fields, including physics, chemistry, and engineering. It provides valuable insights into the behavior of substances and systems and allows for accurate predictions and analyses. By understanding and applying the concepts discussed in this blog post, you can enhance your understanding of internal energy and its applications in different scenarios. Keep exploring and learning, and the world of thermodynamics will continue to unfold before you!

Numerical Problems on how to find internal energy

Problem 1:

Image by MikeRun – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 4.0.

A system undergoes a process in which the work done on the system is 150 J and the heat added to the system is 100 J. Determine the change in internal energy of the system.

Solution:
Given:
Work done on the system, W = 150 J
Heat added to the system, Q = 100 J

The change in internal energy of the system can be calculated using the first law of thermodynamics:

$\Delta U = Q - W$

Substituting the given values, we have:

$\Delta U = 100 \, \text{J} - 150 \, \text{J}$

$\Delta U = -50 \, \text{J}$

Therefore, the change in internal energy of the system is -50 J.

Problem 2:

During a chemical reaction, 500 J of heat is absorbed by the system and 350 J of work is done by the system. Calculate the change in internal energy of the system.

Solution:
Given:
Heat absorbed by the system, Q = 500 J
Work done by the system, W = 350 J

To find the change in internal energy of the system, we use the equation:

$\Delta U = Q - W$

Substituting the given values, we get:

$\Delta U = 500 \, \text{J} - 350 \, \text{J}$

$\Delta U = 150 \, \text{J}$

Therefore, the change in internal energy of the system is 150 J.

Problem 3:

A gas undergoes a process in which 100 J of heat is removed from the system and 75 J of work is done on the system. Calculate the change in internal energy of the system.

Solution:
Given:
Heat removed from the system, Q = -100 J (negative sign indicates heat removal)
Work done on the system, W = 75 J

Using the first law of thermodynamics, we can find the change in internal energy of the system:

$\Delta U = Q - W$

Substituting the given values, we have:

$\Delta U = -100 \, \text{J} - 75 \, \text{J}$

$\Delta U = -175 \, \text{J}$

Therefore, the change in internal energy of the system is -175 J.

Also Read:

TechieScience Core SME

The TechieScience Core SME Team is a group of experienced subject matter experts from diverse scientific and technical fields including Physics, Chemistry, Technology,Electronics & Electrical Engineering, Automotive, Mechanical Engineering. Our team collaborates to create high-quality, well-researched articles on a wide range of science and technology topics for the TechieScience.com website.

All Our Senior SME are having more than 7 Years of experience in the respective fields . They are either Working Industry Professionals or assocaited With different Universities. Refer Our Authors Page to get to know About our Core SMEs.

techiescience.com