Question

How does modern refrigerator takes advantage of the gas law to remove heat from the systems?

Answer 1

We must need to remember that the liquid flows through an expansion device. The exit at its far end is at a low pressure because the compressor is pulling the gas out of that side.
When the liquid HFC hits the low-pressure area, it boils and changes into a gas. The energy required to evaporate the liquid is called the heat of vaporization.

Complete answer:
We need to know that the modern refrigerator takes advantage of the gas laws to remove heat from a system. Compressed gas in the coils is allowed to expand. This expansion lowers the temperature of the gas and transfers heat energy from the material in the refrigerator to the gas. As the gas is pumped through the coils, the pressure on the gas compresses it and raises the gas temperature. This heat is then dissipated through the coils into the outside air. As the compressed gas is pumped through the system again, the process repeats itself.
Modern refrigerators use a gas such as isobutane or a hydrofluorocarbon (HFC) like $1,1,2,2 - tetrafluoroethane$.
A motor and compressor pressurize the gas. According to Gay-Lussac's Law
${P_1}{T_1} = {P_2}{T_2}$
The temperature of a gas increases as the pressure increases. The hot compressed gas flows through the coils on the back or bottom of a refrigerator and heats the condenser coils.
This cools the gas in the coil, and it changes into a liquid because it is under a high pressure.

Note:
Also, according to Gay-Lussac's Law, the decreased pressure of the gas cools it further.
The cold gas moves in the coils through the freezer and refrigerator. The air inside the refrigerator is warmer than the gas in the coil. The air molecules hitting the coil transfer some energy to the coil and then move by convection inside the refrigerator/freezer, where they, in turn, cool the stored food.