## Explanation

### Methods to Remove Energy from Matter

### By Increasing Its Volume

When the volume of a gas increases, its energy is dispersed over a larger area, resulting in a decrease in temperature. The relationship can be represented using the **ideal gas law**:

Where:

- $P$ is the pressure
- $V$ is the volume
- $n$ is the number of moles
- $R$ is the gas constant
- $T$ is the temperature

As the volume $V$ increases, if the pressure $P$ remains constant, the temperature $T$ must decrease, thus lowering the energy.

### By Lowering Its Temperature

**Cooling** a substance directly reduces its molecular kinetic energy. The energy removed follows the **specific heat capacity** formula:

Where:

- $Q$ is the heat or energy removed
- $m$ is the mass
- $c$ is the specific heat capacity
- $\Delta T$ is the change in temperature

Reducing $\Delta T$ will directly lower the internal energy.

### By Increasing Its Pressure

Compressing gas increases its density and can lead to energy removal through **adiabatic compression**, where no heat is exchanged with the surroundings. The energy relationship is given by:

Where:

- $\gamma$ (gamma) is the adiabatic index

### By Boiling It

Evaporating or boiling a liquid removes energy as the **heat of vaporization** is consumed, which is the energy required to turn liquid into gas. This can be demonstrated by:

Where:

- $L_v$ is the latent heat of vaporization

During boiling, energy is taken from the remaining liquid, thus lowering its temperature and energy.

**Optimizing these methods** depends on the physical circumstances and the desired state change of the matter involved.