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relate-work-with-energy-change

๐Ÿš€ Thermodynamics is the branch of physics that deals with the relationships between heat, work, and internal energy. In thermodynamics, we study how energy is transferred and transformed in physical systems. The first law of thermodynamics 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. This relationship can be expressed mathematically as: ฮ”U = Q - W, where ฮ”U is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. Understanding this concept is crucial for analyzing energy changes in various physical processes, such as engines, refrigerators, and other thermodynamic systems.

Theory Explanation

Understanding Internal Energy

Internal energy (U) is the total energy contained within a system due to the kinetic and potential energies of its molecules. It is a state function, meaning it depends only on the current state of the system, not on how it got there.

Heat Transfer (Q)

Heat (Q) is the energy transferred between a system and its surroundings due to a temperature difference. Heat can be added to a system (positive Q) or removed from it (negative Q).

Work Done (W)

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

Applying the First Law of Thermodynamics

The first law of thermodynamics relates the change in internal energy to heat and work. It can be expressed as ฮ”U = Q - W. This equation shows that if heat is added to a system, the internal energy increases, and if work is done by the system, the internal energy decreases.

Key Points

  • ๐ŸŽฏ Thermodynamics studies the relationship between heat, work, and internal energy.
  • ๐ŸŽฏ The first law of thermodynamics states ฮ”U = Q - W.
  • ๐ŸŽฏ Internal energy is a state function and depends on the system's current state.
  • ๐ŸŽฏ Heat can be added or removed from a system, affecting its internal energy.
  • ๐ŸŽฏ Work can be done by or on the system, influencing energy changes.

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Examples:💡

A gas in a piston expands against a constant external pressure of 2 atm, doing 500 J of work. If 1000 J of heat is added to the gas, what is the change in internal energy?

Solution:

Step 1: Identify the values: Q = 1000 J (heat added), W = 500 J (work done by the system).

\[ Q = 1000 \text{ J}, W = 500 \text{ J} \]

Step 2: Apply the first law of thermodynamics: ฮ”U = Q - W.

\[ \Delta U = Q - W = 1000 \text{ J} - 500 \text{ J} \]

Step 3: Calculate the change in internal energy: ฮ”U = 500 J.

\[ \Delta U = 500 \text{ J} \]

A system does 300 J of work on the surroundings and loses 200 J of heat. What is the change in internal energy?

Solution:

Step 1: Identify the values: Q = -200 J (heat lost), W = 300 J (work done by the system).

\[ Q = -200 \text{ J}, W = 300 \text{ J} \]

Step 2: Apply the first law of thermodynamics: ฮ”U = Q - W.

\[ \Delta U = -200 \text{ J} - 300 \text{ J} \]

Step 3: Calculate the change in internal energy: ฮ”U = -500 J.

\[ \Delta U = -500 \text{ J} \]

Common Mistakes

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

    Correction: Always remember the sign convention: Q is positive when heat is added to the system, 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, not the path taken to reach that state.

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

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