In which case would the kinetic energy of particles be increasing?

1. Metal is cooled at 1,300°C.
2. Metal is at room temperature, 37°C
3. Metal is melted at 1,300°C
4. Metal is heated from room temperature to 200°C

The kinetic energy of particles would be increasing in case 4. Metal is being heated from room temperature to 200°C.

The kinetic energy of particles would be increasing in case number 4, when the metal is heated from room temperature to 200°C. Heating the metal causes an increase in the average motion (speed) of the particles, which in turn increases their kinetic energy.

To determine in which case the kinetic energy of particles would be increasing, let's consider the relationship between temperature and the kinetic energy of particles.

The kinetic energy of particles is directly proportional to their temperature. As the temperature of a substance increases, the average kinetic energy of its particles also increases.

Now let's examine the given cases:

1. Metal is cooled at 1,300°C:
In this case, the metal is being cooled, meaning the temperature is decreasing. As a result, the kinetic energy of the metal particles would be decreasing rather than increasing.

2. Metal is at room temperature, 37°C:
At room temperature, the metal is maintaining a constant temperature. Therefore, the kinetic energy of the particles would remain constant. There is neither an increase nor a decrease.

3. Metal is melted at 1,300°C:
When a metal is melted, it undergoes a phase change from a solid to a liquid. During this process, energy is added to the metal to overcome the intermolecular forces holding the particles together. This added energy increases the kinetic energy of the particles. So, in this case, the kinetic energy of the metal particles would be increasing.

4. Metal is heated from room temperature to 200°C:
In this scenario, the metal is being heated. As the temperature increases, so does the kinetic energy of the particles. Therefore, the metal particles' kinetic energy would be increasing.

In conclusion, cases 3 and 4 would result in an increase in the kinetic energy of the metal particles.