Short Answer:
The first law of thermodynamics applies to heat exchangers by explaining how energy is conserved during the heat transfer between two fluids. In a heat exchanger, one fluid gives heat, and the other fluid absorbs it. There is no work done, and the system is designed to exchange heat without any loss to the surroundings.
This law helps calculate how much heat is gained or lost by the fluids and ensures that the total energy entering the control volume is equal to the total energy leaving. It is commonly used in designing boilers, condensers, radiators, air conditioning units, and many industrial cooling systems.
Detailed Explanation:
First law of thermodynamics in heat exchangers
A heat exchanger is a device used to transfer heat from one fluid to another without mixing them. This process is widely used in industries, power plants, refrigeration systems, and HVAC units. The first law of thermodynamics, also called the law of energy conservation, is used to analyze and design these systems effectively.
According to this law, energy can neither be created nor destroyed, it can only be transferred from one form to another. In heat exchangers, energy is transferred as heat from a hot fluid to a cold fluid, and the total heat lost by the hot fluid is equal to the total heat gained by the cold fluid.
Energy Balance in a Heat Exchanger
The control volume in a heat exchanger includes the region where the two fluids flow and exchange heat. The first law for steady-flow systems can be written as:
Q̇ – Ẇ = ṁ × (h₂ – h₁ + (V₂² – V₁²)/2 + g(Z₂ – Z₁))
But for heat exchangers:
- There is no work done (Ẇ = 0)
- Changes in kinetic and potential energy are usually negligible
- Heat transfer is internal between two fluids (not from surroundings)
So, the simplified equation becomes:
ṁ_hot × (h₁ – h₂) = ṁ_cold × (h₄ – h₃)
Where:
- ṁ_hot = mass flow rate of hot fluid
- ṁ_cold = mass flow rate of cold fluid
- h₁, h₂ = inlet and outlet enthalpies of hot fluid
- h₃, h₄ = inlet and outlet enthalpies of cold fluid
This equation means that the heat lost by the hot fluid equals the heat gained by the cold fluid, assuming no heat is lost to the environment.
Key Points of Heat Exchanger Analysis
- No work interaction
Heat exchangers do not involve any moving parts doing work. The energy transfer is purely in the form of heat. - Steady flow assumption
Most heat exchangers work under steady-flow conditions, where mass and energy flow remain constant with time. - Negligible heat loss to surroundings
Good insulation is used to ensure all heat is transferred between the fluids only. - Internal energy change
The internal energy of each fluid changes due to the gain or loss of heat. - Enthalpy difference
Since pressure changes are small, the change in enthalpy is a good indicator of heat transfer.
Common Types of Heat Exchangers
- Shell and Tube Heat Exchangers
Used in industries and power plants for large-scale heat exchange. - Plate Heat Exchangers
Compact units used in HVAC and food processing systems. - Air Cooled Heat Exchangers
Used where water is not available, such as in radiators.
In all these types, the first law is used to calculate heat balance, ensuring the energy lost by one fluid is exactly gained by the other.
Applications in Real Systems
- Boilers and Condensers: Steam and water exchange heat in thermal power stations.
- Radiators in Cars: Engine coolant transfers heat to the air.
- Evaporators and Condensers in AC Units: Refrigerants absorb or release heat to condition the air.
- Industrial Cooling Systems: Maintain machinery temperatures within safe limits.
By applying the first law, engineers can find the required surface area, mass flow rate, and temperature changes for the desired heat transfer.
Conclusion
The first law of thermodynamics applies to heat exchangers by showing how heat energy is conserved between two fluids. It states that the heat lost by the hot fluid equals the heat gained by the cold fluid, assuming no energy is lost to the surroundings. This law is very important in designing and analyzing heat exchangers used in various mechanical and industrial systems for efficient energy management.