91Ó°ÊÓ

When the internal energy of a system changes, it is often due to external influences such as heat transfer or work being done on the system. In our context, internal energy (\(\Delta U\)) is the energy contained within the system itself. This exercise uses the First Law of Thermodynamics, which relates internal energy change to heat and work. For any system:\[\Delta U = Q - W\]where \(Q\) is the heat added to the system, and \(W\) is the work done by the system.In this problem, since no heat is exchanged (\(Q = 0\)), the change in internal energy is solely from the work. Thus, when work is done on the system, internal energy increases. The exercise clarifies this with a calculation showing the energy increase by 457 J.

An ideal gas is a theoretical gas composed of many randomly moving point particles that interact only through elastic collisions. This concept is crucial because it simplifies many calculations in thermodynamics. Ideal gases follow the ideal gas law, expressed as:\[PV = nRT\]where \(P\) is pressure, \(V\) is volume, \(n\) is the amount of moles, \(R\) is the universal gas constant, and \(T\) is temperature.In this exercise, helium gas (He) is typically treated as an ideal gas. This assumption allows us to focus on key work and energy changes without complex molecular interactions affecting our calculations. It's important to remember that while ideal gas behavior provides a good approximation for many gases, real gases may deviate from this ideal behavior under certain conditions.

The concept of work in thermodynamics can be thought of as energy transfer to or from a system through force applied over distance. Work done on a gas is especially important in changing its internal energy.

• When work is done on the gas, energy is added to the system, and the internal energy increases.
• If the system does work on the surroundings, energy is lost, and internal energy decreases.

In this exercise, 457 J of work is done on the helium gas. Following the convention where work done on the system is negative (as energy is added to the system), we relate this to the increase in internal energy. Thus, knowing the work done provides a direct measure of how much the internal energy changes.

Thermodynamics is the branch of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and physical properties of matter. Its principles are fundamental in explaining how energy transfers and transformations occur. The First Law of Thermodynamics applies here as it equates changes in internal energy to heat and work. It helps us understand that:

• Energy within a closed system is conserved. Any energy change in the system is due to transfers of energy by heat or work.
• The law can predict how energy will transfer even in more complex interactions.

Applying the First Law allows us to determine the change in internal energy by considering work done on the gas. Recognizing that no heat is exchanged due to insulation further simplifies this problem. The First Law forms the backbone for many calculations across various applications in science and engineering.