Let's break down the concepts surrounding the internal energy of gases and how it relates to heat and temperature. The statements you've provided touch on various principles of thermodynamics, so I'll clarify each one to help you understand their implications.
Understanding Internal Energy
Internal energy is a measure of the total energy contained within a system, which includes kinetic energy from the motion of particles and potential energy from the interactions between them. For gases, this energy is primarily related to the kinetic energy of the molecules, which is influenced by temperature.
Analyzing Each Statement
- A) Whenever heat is supplied to a gas, its internal energy increases.
This statement is generally true. When heat is added to a gas, it typically increases the kinetic energy of the gas molecules, leading to an increase in internal energy. However, it's important to note that this energy can also be used for work done by the gas, such as expanding against a piston, which might not directly increase internal energy.
- B) Internal energy of a gas must increase when its temperature is increased.
This is also true. The temperature of a gas is directly related to the average kinetic energy of its molecules. As temperature rises, the kinetic energy increases, which in turn raises the internal energy of the gas. This relationship is a fundamental principle of thermodynamics.
- C) Internal energy of a gas may be increased even if heat is not supplied to the gas.
This statement can be true in certain scenarios. For example, if a gas is compressed, work is done on it, which can increase its internal energy without any heat being added. This is described by the first law of thermodynamics, which states that the change in internal energy is equal to the heat added to the system minus the work done by the system.
- D) Internal energy of a gas may be proportional to the square of the velocity of the vessel in which it is contained.
This statement is misleading. The internal energy of a gas is not directly proportional to the square of the velocity of the vessel. Instead, it is related to the average kinetic energy of the gas molecules themselves, which depends on their speed and mass, not the speed of the container. The kinetic energy of the gas molecules is given by the equation KE = 1/2 mv², where m is the mass and v is the velocity of the molecules.
Key Takeaways
In summary, the internal energy of a gas is closely tied to its temperature and the kinetic energy of its molecules. Heat transfer generally increases internal energy, but work done on the gas can also contribute to this energy change. Understanding these principles is crucial for grasping the behavior of gases in various thermodynamic processes.
