College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
Peak speed is the most probable speed of particles in a gas at a given temperature, as described by the Maxwell-Boltzmann distribution. It is the speed at which the greatest number of particles are moving in a system.
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Peak speed increases with temperature because higher temperatures provide more kinetic energy to the particles.
The peak speed can be calculated using the formula $v_{mp} = \sqrt{\frac{2k_B T}{m}}$, where $v_{mp}$ is the most probable speed, $k_B$ is Boltzmann's constant, $T$ is the temperature, and $m$ is the mass of a gas particle.
In a Maxwell-Boltzmann distribution graph, peak speed corresponds to the highest point on the curve.
For heavier gas molecules, the peak speed will be lower at a given temperature compared to lighter molecules.
Peak speed differs from average and root mean square speeds but all three speeds increase as temperature increases.
Review Questions
How does peak speed change with an increase in temperature for a gas?
What formula would you use to calculate peak speed and what do each of its components represent?
In what way does the mass of gas particles affect their peak speed?
Related terms
Maxwell-Boltzmann Distribution: A probability distribution that describes the distribution of speeds among particles in a gas.
Average Speed: The mean speed of all particles in a gas sample, calculated by summing all individual speeds and dividing by the number of particles.
Root Mean Square Speed: $v_{rms} = \sqrt{\frac{3k_B T}{m}}$, representing an effective value for particle speeds that accounts for both magnitude and direction.