Short Answer:

The first law of thermodynamics applies to compressors by explaining how energy is conserved during the compression of a gas. In a compressor, mechanical work is done on the gas, increasing its pressure, temperature, and internal energy. The energy added as work is stored in the gas or released as heat.

This law helps in analyzing how much work is needed to compress a gas and how the internal energy and enthalpy of the gas change. It is useful for designing efficient compressors used in refrigeration, air conditioning, gas pipelines, and engines.

Detailed Explanation:

First law of thermodynamics in compressors

The first law of thermodynamics is also called the law of energy conservation, which states that energy cannot be created or destroyed but only converted from one form to another. When applied to compressors, this law helps us understand how mechanical energy (work input) is transferred into the internal energy and enthalpy of the gas being compressed.

A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. It works by supplying external work (from an electric motor or engine) to compress the gas. As the gas is compressed, its internal energy increases, and it often becomes hotter unless cooled.

Energy Balance in a Compressor

When applying the first law to a steady-flow process like a compressor, the energy balance equation is written as:

Q̇ – Ẇ = ṁ × (h₂ – h₁ + (V₂² – V₁²)/2 + g(Z₂ – Z₁))

Where:

• Q̇ = Heat added to the gas
• Ẇ = Work done on the gas (input work)
• ṁ = Mass flow rate of gas
• h = Specific enthalpy
• V²/2 = Kinetic energy
• gZ = Potential energy

For most compressors:

• Change in kinetic and potential energy is small → ignored
• Heat loss to surroundings may or may not be considered depending on insulation

So, the simplified form becomes:

Ẇ = ṁ × (h₂ – h₁)

This equation tells us that the work done on the gas is used to increase its enthalpy, which includes internal energy and flow energy.

Key Effects of Compression

1. Pressure Increase:
   The gas pressure rises because work is done to force the gas into a smaller volume.
2. Temperature Rise:
   As internal energy increases, the temperature of the gas also increases unless cooled by an intercooler or heat exchanger.
3. Volume Reduction:
   Compressors reduce the volume of gas, which results in an increase in pressure as per Boyle’s Law.
4. Work Input:
   The energy needed to operate the compressor comes from an external power source, and this is calculated using the first law.

Types of Compressors Using First Law

• Reciprocating Compressors:
  Use pistons to compress gas. Common in refrigerators and gas plants.
• Rotary Compressors:
  Use rotating vanes or screws. Used in air conditioners and industrial systems.
• Centrifugal Compressors:
  Use high-speed rotating blades. Used in gas turbines and jet engines.

In each type, the first law of thermodynamics helps calculate the amount of energy needed and how the gas behaves during compression.

Real-Life Applications

The first law helps engineers in:

• Designing compressors that use less power
• Calculating heat rejection and cooling requirements
• Predicting temperature rise after compression
• Improving efficiency of refrigeration and air conditioning cycles

In systems like refrigerators, car engines, and air compressors, understanding how energy flows using the first law is essential for performance improvement.

Conclusion

The first law of thermodynamics applies to compressors by showing how mechanical work input increases the internal energy and enthalpy of the gas. It helps calculate how much energy is required to compress gases, and it is crucial in designing efficient and reliable systems. This law ensures that engineers understand the complete energy conversion during the compression process.