Class 11 >> Physics >> thermodynamics >> first-law-of-thermodynamics >> state-the-first-law-of-thermodynamics
Skip to Practice

state-the-first-law-of-thermodynamics

๐Ÿš€ The First Law of Thermodynamics is a fundamental principle that describes the relationship between heat, work, and internal energy in a thermodynamic system. It states that energy cannot be created or destroyed, only transformed from one form to another. This law is often 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 means that if a system absorbs heat, its internal energy increases, and if it does work on its surroundings, its internal energy decreases.

Theory Explanation

Understanding Internal Energy

Internal energy 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 got there.

Heat Transfer (Q)

Heat (Q) is the energy transferred between the system and its surroundings due to a temperature difference. When heat is added to the system, it increases the internal energy.

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

The First Law can be applied to various processes, such as isothermal, adiabatic, and isochoric processes, to analyze how energy is conserved and transformed.

Key Points

  • ๐ŸŽฏ Energy is conserved in a closed system.
  • ๐ŸŽฏ The First Law relates heat, work, and internal energy.
  • ๐ŸŽฏ Internal energy is a state function and depends only on the state of the system.
  • ๐ŸŽฏ Work done by the system is considered positive, while work done on the system is negative.
  • ๐ŸŽฏ Heat transfer can occur in different forms: conduction, convection, and radiation.

๐Ÿ›  Simulation is being generated. Please check back in a few moments.

Examples:💡

A gas in a piston expands against a constant external pressure of 2 atm, absorbing 500 J of heat. Calculate the change in internal energy if the gas does 300 J of work.

Solution:

Step 1: Identify the values: Q = 500 J (heat absorbed), W = 300 J (work done by the gas).

\[ Q = 500, W = 300 \]

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

\[ ฮ”U = 500 - 300 \]

Step 3: Calculate ฮ”U: ฮ”U = 200 J.

\[ ฮ”U = 200 J \]

In an adiabatic process, a gas does 400 J of work on the surroundings. If the internal energy decreases by 200 J, how much heat is exchanged with the surroundings?

Solution:

Step 1: Since the process is adiabatic, Q = 0. Use the First Law: ฮ”U = Q - W.

\[ ฮ”U = 0 - 400 \]

Step 2: Rearranging gives Q = ฮ”U + W. Substitute ฮ”U = -200 J and W = 400 J.

\[ Q = -200 + 400 \]

Step 3: Calculate Q: Q = 200 J (heat is lost to the surroundings).

\[ Q = 200 J \]

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: W is positive when work is done by the system and negative when done on the system.

  • Mistake: Not recognizing that internal energy is a state function. Students may think it depends on the path taken.

    Correction: Internal energy depends only on the current state of the system, not on how it reached that state.

  • Mistake: Misapplying the First Law in processes where heat transfer is not considered, such as in adiabatic processes.

    Correction: In adiabatic processes, remember that Q = 0, and apply the First Law accordingly.

โ† Back Start Practice