Answer :
To determine the average kinetic energy of the particles in a substance made up of 1,000 particles, you need to consider all the individual kinetic energies of each particle and find their average.
1. Total Kinetic Energy: First, the total kinetic energy of the particles is the sum of the kinetic energies of all 1,000 particles.
2. Averaging Process: To find the average kinetic energy per particle, divide the total kinetic energy by the number of particles, which in this case is 1,000.
Mathematically, if [tex]\( KE_1, KE_2, KE_3, \ldots, KE_{1000} \)[/tex] are the kinetic energies of the 1,000 particles, then:
[tex]\[ \text{Total Kinetic Energy} = KE_1 + KE_2 + KE_3 + \ldots + KE_{1000} \][/tex]
The average kinetic energy, [tex]\( \overline{KE} \)[/tex], is given by:
[tex]\[ \overline{KE} = \frac{KE_1 + KE_2 + KE_3 + \ldots + KE_{1000}}{1000} \][/tex]
Given the objective is to describe the average kinetic energy of the particles, we look through the provided options:
- The total kinetic energy of the particles plus 1,000: This option describes an addition operation rather than an averaging process.
- The kinetic energy of the fastest particle multiplied by 1,000: This option emphasizes a single particle's energy rather than the average energy of all particles.
- The sum of the particles' kinetic energies divided by 1,000: This option accurately represents the process of averaging, where the total kinetic energy is divided by the number of particles.
Hence, the correct description of the average kinetic energy of the particles is:
The sum of the particles' kinetic energies divided by 1,000.
1. Total Kinetic Energy: First, the total kinetic energy of the particles is the sum of the kinetic energies of all 1,000 particles.
2. Averaging Process: To find the average kinetic energy per particle, divide the total kinetic energy by the number of particles, which in this case is 1,000.
Mathematically, if [tex]\( KE_1, KE_2, KE_3, \ldots, KE_{1000} \)[/tex] are the kinetic energies of the 1,000 particles, then:
[tex]\[ \text{Total Kinetic Energy} = KE_1 + KE_2 + KE_3 + \ldots + KE_{1000} \][/tex]
The average kinetic energy, [tex]\( \overline{KE} \)[/tex], is given by:
[tex]\[ \overline{KE} = \frac{KE_1 + KE_2 + KE_3 + \ldots + KE_{1000}}{1000} \][/tex]
Given the objective is to describe the average kinetic energy of the particles, we look through the provided options:
- The total kinetic energy of the particles plus 1,000: This option describes an addition operation rather than an averaging process.
- The kinetic energy of the fastest particle multiplied by 1,000: This option emphasizes a single particle's energy rather than the average energy of all particles.
- The sum of the particles' kinetic energies divided by 1,000: This option accurately represents the process of averaging, where the total kinetic energy is divided by the number of particles.
Hence, the correct description of the average kinetic energy of the particles is:
The sum of the particles' kinetic energies divided by 1,000.
