The domestic refrigerator operates on the vapor compression cycle, which is a common refrigeration cycle used in refrigerators and air conditioning systems. One of the key components of this cycle is the device used for expansion. In the case of a domestic refrigerator, the device used for expansion is a capillary tube.

Explanation:
1. Vapor Compression Cycle: The vapor compression cycle is a thermodynamic cycle that uses the properties of a refrigerant to cool a space or maintain a low temperature. It consists of four main components: compressor, condenser, expansion device, and evaporator.

2. The Role of the Expansion Device: The expansion device plays a crucial role in the vapor compression cycle. It is responsible for reducing the pressure of the refrigerant and controlling its flow rate into the evaporator. This reduction in pressure causes the refrigerant to undergo a phase change from a high-pressure liquid to a low-pressure vapor.

3. Types of Expansion Devices: There are several types of expansion devices used in refrigeration systems, including thermostatic valves, thermostats, capillary tubes, and throttling valves. Each type has its own advantages and applications, but in the case of a domestic refrigerator, a capillary tube is commonly used.

4. Capillary Tube: A capillary tube is a small-diameter tube made of copper or other materials. It is a simple and inexpensive device used for expansion in refrigeration systems. The capillary tube has a very small internal diameter, typically ranging from 0.5 to 2 mm, which creates a high-pressure drop and restricts the flow of refrigerant.

5. Working Principle of Capillary Tube: The capillary tube works based on the principle of pressure difference. The high-pressure liquid refrigerant enters the capillary tube from the condenser side, and as it flows through the tube, the pressure drops significantly. This pressure drop causes the refrigerant to expand and evaporate, absorbing heat from the surrounding air in the evaporator.

6. Advantages of Capillary Tube: The capillary tube has several advantages in domestic refrigerators. It is a simple and reliable device with no moving parts, which reduces the chances of failure. It also provides a constant and controlled flow of refrigerant, allowing for efficient heat transfer in the evaporator.

In conclusion, the domestic refrigerator operating on the vapor compression cycle uses a capillary tube as the expansion device. The capillary tube is a small-diameter tube that reduces the pressure of the refrigerant and controls its flow into the evaporator. It is a simple and reliable device that ensures efficient heat transfer in the evaporator, making it suitable for domestic refrigeration applications.