To determine which sample has the higher temperature, we need to consider the relationship between temperature and the kinetic energy of gas particles.
Temperature is a measure of the average kinetic energy of the particles in a substance. The equation for the average kinetic energy (KE) of a particle is given by:
\[ KE = \frac{1}{2}mv^2 \]
where \( m \) is the mass of the particle and \( v \) is the speed of the particle.
In this case, both samples (A and B) have particles moving at the same average speed. However, the mass of particles in sample A is less than the mass of particles in sample B.
Since the average speed is the same for both samples, the average kinetic energy can be expressed more generally. For sample A, with lighter particles, the lower mass means that the kinetic energy will be relatively lower compared to sample B, where the particles have greater mass.
To compare the average kinetic energies:
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Sample A:
- Lower mass (m), same speed (v), so its average kinetic energy is lower than that of sample B.
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Sample B:
- Higher mass (m), same speed (v), so its average kinetic energy is higher than that of sample A.
Therefore, since sample B has particles with greater mass moving at the same average speed, it will have a higher average kinetic energy than sample A.
Thus, the correct answer is:
B. sample B; its particles have the higher average kinetic energy.
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