How does the first law of thermodynamics apply to a closed system?

Short Answer

The First Law of Thermodynamics applies to a closed system by stating that the total energy remains constant, and any heat added to the system is either stored as internal energy or used to perform work. A closed system allows energy transfer in the form of heat and work but does not allow mass transfer.

For a closed system, the First Law is expressed as:

Q=ΔU+WQ = \Delta U + WQ=ΔU+W

where Q is the heat supplied, ΔU is the change in internal energy, and W is the work done. This principle is used in piston-cylinder devices, boilers, and pressure vessels to analyze heat and energy interactions.

Detailed Explanation

First Law of Thermodynamics in a Closed System

A closed system is a system that allows energy transfer but does not permit the transfer of mass across its boundary. The First Law of Thermodynamics governs how energy behaves in such a system.

Energy Balance in a Closed System

The First Law equation for a closed system is:

Q=ΔU+WQ = \Delta U + WQ=ΔU+W

Where:

  • Q = Heat energy supplied to the system (Joules)
  • ΔU = Change in internal energy of the system (Joules)
  • W = Work done by or on the system (Joules)

This equation means:

  • If heat is added to the system, it increases internal energy or is used to perform work.
  • If work is done on the system, it increases the internal energy.
  • If the system does work on the surroundings, internal energy decreases.

Different Processes in a Closed System

  1. Constant Volume Process (Isochoric Process)
    • W = 0, so the equation simplifies to Q = ΔU.
    • All heat added increases internal energy since no work is done.
    • Example: Gas in a rigid container being heated.
  2. Constant Pressure Process (Isobaric Process)
    • Some heat is used to increase internal energy, and some is used to do work.
    • Example: Steam formation in a boiler.
  3. Adiabatic Process (No Heat Transfer)
    • Q = 0, so the equation becomes ΔU = -W.
    • Work is done at the cost of internal energy.
    • Example: Compression or expansion of gas in an insulated cylinder.
  4. Cyclic Process (Energy Balance Over a Cycle)
    • Since ΔU = 0, the equation simplifies to Q = W.
    • Heat input is completely converted into work output.
    • Example: Carnot cycle, Rankine cycle.

Applications of the First Law in a Closed System

  • Internal Combustion Engines: Fuel burns inside a closed cylinder, releasing heat and doing work.
  • Piston-Cylinder Devices: Work is done as gas expands or compresses inside the cylinder.
  • Refrigeration and Air Conditioning: The refrigerant undergoes heat transfer within a closed loop.
Conclusion

The First Law of Thermodynamics applies to a closed system by ensuring that the heat added is either converted into work or stored as internal energy. In a closed system, energy transfer occurs without mass flow, making this principle essential in thermodynamic analysis of engines, compressors, and boilers.