In a gas kept at a constant temperature, all molecules move with the same speed.
True or False?
I believe that is true because the pressure would be equal if the temperature is so the molecules would have the same speed.
The AVERAGE speed might be the same but I don't believe ALL of them would have the same speed.
can someone help with math
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The statement is false. In a gas kept at a constant temperature, molecules have a distribution of speeds, not all moving with the same speed. This is due to the Maxwell-Boltzmann distribution, which describes the statistical distribution of speeds among gas molecules.
To understand why this is the case, it's helpful to consider the kinetic theory of gases. According to this theory, the molecules in a gas are in constant, random motion. The temperature of a gas is a measure of the average kinetic energy of its molecules.
At a given temperature, the average kinetic energy is the same for all gas molecules. However, individual molecules can have different velocities, resulting in a range of speeds. Some molecules might have higher velocities (and therefore higher speeds), while others might have lower velocities.
The Maxwell-Boltzmann distribution describes how the speeds of gas molecules are distributed at a given temperature. It shows that there is a most probable speed, but also a range of speeds around it. This means that while some molecules may have speeds close to the most probable speed, others will have speeds that are higher or lower.
So, in a gas kept at a constant temperature, not all molecules move with the same speed. They have a distribution of speeds described by the Maxwell-Boltzmann distribution.