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apply-first-law-in-closed-systems

๐Ÿš€ The First Law of Thermodynamics, also known as the Law of Energy Conservation, states that energy cannot be created or destroyed in an isolated system. Instead, energy can only be transformed from one form to another. In the context of closed systems, this law can be expressed mathematically as ฮ”U = Q - W, where ฮ”U is the change in internal energy of the system, Q is the heat added to the system, and W is the work done by the system. This principle is fundamental in understanding how energy flows and changes form in physical processes.

Theory Explanation

Understanding Internal Energy

Internal energy (U) is the total energy contained within a system, including kinetic and potential energy at the molecular level. It is a state function, meaning it depends only on the current state of the system, not on how it reached that state.

Heat Transfer (Q)

Heat (Q) is the energy transferred into or out of a system due to a temperature difference. When heat is added to a system, it increases the internal energy, while heat removed decreases it.

Work Done (W)

Work (W) is the energy transferred when a force is applied over a distance. In thermodynamics, work can be done by the system (expansion) or on the system (compression). The sign convention is important: work done by the system is positive, while work done on the system is negative.

Applying the First Law

To apply the First Law in closed systems, you can rearrange the equation ฮ”U = Q - W to find any of the three variables if the other two are known. This allows for the analysis of energy changes in various thermodynamic processes.

Key Points

  • ๐ŸŽฏ Energy is conserved in closed systems.
  • ๐ŸŽฏ Internal energy is a state function.
  • ๐ŸŽฏ Heat added to the system increases internal energy.
  • ๐ŸŽฏ Work done by the system decreases internal energy.
  • ๐ŸŽฏ The First Law can be applied to analyze energy changes.

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Examples:💡

A gas in a closed container absorbs 500 J of heat and does 200 J of work on the surroundings. Calculate the change in internal energy of the gas.

Solution:

Step 1: Identify the values: Q = 500 J (heat added), W = 200 J (work done by the system).

\[ Q = 500, W = 200 \]

Step 2: Apply the First Law of Thermodynamics: ฮ”U = Q - W.

\[ ฮ”U = 500 - 200 \]

Step 3: Calculate the change in internal energy: ฮ”U = 300 J.

\[ ฮ”U = 300 J \]

In a closed system, 300 J of heat is removed from the system, and 100 J of work is done on the system. Find the change in internal energy.

Solution:

Step 1: Identify the values: Q = -300 J (heat removed), W = -100 J (work done on the system).

\[ Q = -300, W = -100 \]

Step 2: Apply the First Law of Thermodynamics: ฮ”U = Q - W.

\[ ฮ”U = -300 - (-100) \]

Step 3: Calculate the change in internal energy: ฮ”U = -300 + 100 = -200 J.

\[ ฮ”U = -200 J \]

Common Mistakes

  • Mistake: Confusing the signs of heat and work. Students often forget that heat added is positive and work done by the system is positive.

    Correction: Always remember the sign conventions: Q is positive when heat is added, and W is positive when work is done by the system.

  • Mistake: Not recognizing that internal energy is a state function and depends only on the current state of the system.

    Correction: Focus on the initial and final states of the system when calculating changes in internal energy.

  • Mistake: Misapplying the First Law by not accounting for all forms of energy transfer.

    Correction: Ensure that all heat and work interactions are included in the calculations.

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