A Piston Contains A Diatomic Gas. The Piston Expands As The Gas Does 109 J Of Work While 244 J Of Heat Are Added. What Is The Change In Internal Energy?${ \begin{aligned} \Delta U & =[?] , J \ \Delta U & = Q - W \end{aligned} }$Where:-
Introduction
In thermodynamics, the change in internal energy of a system is a fundamental concept that plays a crucial role in understanding various physical processes. The internal energy of a system is a measure of the total energy associated with the motion of its particles, including both kinetic energy and potential energy. In this article, we will explore the concept of change in internal energy, specifically in the context of a piston containing a diatomic gas.
The First Law of Thermodynamics
The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only converted from one form to another. Mathematically, this is expressed as:
ΔU = Q - W
where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
Work Done by the System
In the context of a piston containing a diatomic gas, the work done by the system is a critical component in determining the change in internal energy. As the piston expands, the gas does 109 J of work. This work is a result of the gas's ability to exert a force on the piston, causing it to move.
Heat Added to the System
In addition to the work done by the system, heat is also added to the system. In this case, 244 J of heat are added to the system. This heat energy is transferred to the system through various means, such as conduction, convection, or radiation.
Change in Internal Energy
Now that we have a clear understanding of the work done by the system and the heat added to the system, we can proceed to calculate the change in internal energy. Using the first law of thermodynamics, we can write:
ΔU = Q - W ΔU = 244 J - 109 J ΔU = 135 J
Therefore, the change in internal energy of the system is 135 J.
Discussion
The change in internal energy of a system is a critical concept in thermodynamics, as it provides insight into the energy transformations that occur within the system. In the context of a piston containing a diatomic gas, the change in internal energy is influenced by both the work done by the system and the heat added to the system.
Conclusion
In conclusion, the change in internal energy of a system can be calculated using the first law of thermodynamics. By understanding the work done by the system and the heat added to the system, we can determine the change in internal energy. In this article, we have explored the concept of change in internal energy, specifically in the context of a piston containing a diatomic gas.
References
- [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
- [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
Mathematical Derivation
To derive the change in internal energy, we can start with the first law of thermodynamics:
ΔU = Q - W
where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
We can then substitute the given values for Q and W:
ΔU = 244 J - 109 J ΔU = 135 J
Therefore, the change in internal energy of the system is 135 J.
Additional Information
- Diatomic Gas: A diatomic gas is a type of gas that consists of molecules composed of two atoms. Examples of diatomic gases include oxygen (O2) and nitrogen (N2).
- Piston: A piston is a movable component that is used to transfer energy from one system to another. In the context of a piston containing a diatomic gas, the piston is used to expand the gas, causing it to do work.
- Work: Work is a measure of the energy transferred from one system to another through a force applied over a distance. In the context of a piston containing a diatomic gas, the work done by the system is a result of the gas's ability to exert a force on the piston, causing it to move.
A Piston Containing a Diatomic Gas: Understanding the Change in Internal Energy ===========================================================
Q&A: Frequently Asked Questions
Q: What is the change in internal energy of a system?
A: The change in internal energy of a system is a measure of the total energy associated with the motion of its particles, including both kinetic energy and potential energy.
Q: How is the change in internal energy calculated?
A: The change in internal energy is calculated using the first law of thermodynamics, which states that energy cannot be created or destroyed, only converted from one form to another. Mathematically, this is expressed as:
ΔU = Q - W
where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
Q: What is the significance of the first law of thermodynamics?
A: The first law of thermodynamics is a fundamental principle that states that energy cannot be created or destroyed, only converted from one form to another. This principle is essential in understanding various physical processes, including the change in internal energy of a system.
Q: What is the difference between work and heat?
A: Work and heat are two different forms of energy transfer. Work is a measure of the energy transferred from one system to another through a force applied over a distance, while heat is a measure of the energy transferred from one system to another through thermal interactions.
Q: How does the change in internal energy relate to the work done by the system?
A: The change in internal energy is directly related to the work done by the system. As the system does work, its internal energy changes. The amount of change in internal energy is determined by the amount of work done by the system.
Q: What is the significance of the change in internal energy in a piston containing a diatomic gas?
A: The change in internal energy in a piston containing a diatomic gas is significant because it provides insight into the energy transformations that occur within the system. By understanding the change in internal energy, we can determine the amount of energy transferred from one system to another.
Q: Can the change in internal energy be negative?
A: Yes, the change in internal energy can be negative. This occurs when the system loses energy to its surroundings, resulting in a decrease in its internal energy.
Q: What is the relationship between the change in internal energy and the heat added to the system?
A: The change in internal energy is directly related to the heat added to the system. As heat is added to the system, its internal energy changes. The amount of change in internal energy is determined by the amount of heat added to the system.
Q: Can the change in internal energy be zero?
A: Yes, the change in internal energy can be zero. This occurs when the system is in a state of equilibrium, and no energy is transferred from one system to another.
Q: What is the significance of the change in internal energy in real-world applications?
A: The change in internal energy is significant in various real-world applications, including power generation, refrigeration, and air conditioning. By understanding the change in internal energy, we can design more efficient systems that minimize energy losses and maximize energy gains.
Conclusion
In conclusion, the change in internal energy of a system is a critical concept in thermodynamics that provides insight into the energy transformations that occur within the system. By understanding the change in internal energy, we can design more efficient systems that minimize energy losses and maximize energy gains.
References
- [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
- [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.
Additional Information
- Diatomic Gas: A diatomic gas is a type of gas that consists of molecules composed of two atoms. Examples of diatomic gases include oxygen (O2) and nitrogen (N2).
- Piston: A piston is a movable component that is used to transfer energy from one system to another. In the context of a piston containing a diatomic gas, the piston is used to expand the gas, causing it to do work.
- Work: Work is a measure of the energy transferred from one system to another through a force applied over a distance. In the context of a piston containing a diatomic gas, the work done by the system is a result of the gas's ability to exert a force on the piston, causing it to move.