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learn-about-internal-energy-of-a-system

๐Ÿš€ Thermodynamics is the branch of physics that deals with the relationships between heat, work, and internal energy in a system. Internal energy is the total energy contained within a system, which includes kinetic and potential energy at the molecular level. Understanding the internal energy of a system is crucial for analyzing how energy is transferred and transformed in physical processes. 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 on its surroundings. This relationship is fundamental in understanding energy conservation in thermodynamic processes.

Theory Explanation

Understanding Internal Energy

Internal energy (U) is the sum of all microscopic forms of energy in a system, including kinetic energy of molecules and potential energy due to intermolecular forces. It is a state function, meaning it depends only on the current state of the system, not on how it reached that state.

\[ U = U_{initial} + Q - W \]
First Law of Thermodynamics

The first law of thermodynamics 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. This law emphasizes the conservation of energy, stating that energy cannot be created or destroyed, only transformed from one form to another.

\[ \Delta U = Q - W \]
Heat Transfer and Work

Heat (Q) is the energy transferred due to a temperature difference, while work (W) is the energy transferred when a force is applied over a distance. In thermodynamic processes, heat can be added to or removed from a system, and work can be done on or by the system, affecting its internal energy.

Key Points

  • ๐ŸŽฏ Internal energy is a state function dependent on the system's current state.
  • ๐ŸŽฏ The first law of thermodynamics relates internal energy, heat, and work.
  • ๐ŸŽฏ Heat transfer occurs due to temperature differences, while work involves force and distance.

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Examples:💡

A gas in a piston expands against a constant external pressure of 5 atm, doing 200 J of work. If 500 J of heat is added to the gas, what is the change in internal energy?

Solution:

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

\[ Q = 500 \text{ J}, W = 200 \text{ J} \]

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

\[ \Delta U = 500 \text{ J} - 200 \text{ J} = 300 \text{ J} \]

Step 3: The change in internal energy is 300 J.

Common Mistakes

  • Mistake: Confusing heat (Q) with work (W) and not recognizing their different roles in energy transfer.

    Correction: Remember that heat is energy transfer due to temperature difference, while work is energy transfer due to force applied over a distance.

  • Mistake: Forgetting that internal energy is a state function and depends only on the current state of the system.

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

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