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What happens to the peak of the curve in the Maxwell-Boltzmann distribution graph if temperature increases?
- a)Shifts forward and upward
- b)Shifts forward and downward
- c)Shifts backward and upward
- d)Shifts backward and downward
Correct answer is option 'B'. Can you explain this answer?
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What happens to the peak of the curve in the Maxwell-Boltzmann distrib...
With the increase of temperature, the peak shifts forward but downward. This is because with the increase of temperature, the most probable kinetic energy increases and the fraction of molecules possessing most probable kinetic energy decreases.
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What happens to the peak of the curve in the Maxwell-Boltzmann distrib...
Explanation:
The Maxwell-Boltzmann distribution graph represents the distribution of speeds of particles in a gas at a given temperature. The graph is a smooth, bell-shaped curve, with the peak of the curve representing the most probable speed of the particles.
When the temperature of the gas increases, the peak of the curve shifts forward and downward. This means that the most probable speed of the particles increases, but the overall distribution becomes broader.
Effect of temperature on the shape of the curve:
- Higher temperature: At higher temperatures, the particles in the gas have more kinetic energy. This leads to an increase in the average speed of the particles and a broader distribution of speeds. As a result, the peak of the curve shifts forward, indicating a higher most probable speed.
- Lower temperature: At lower temperatures, the particles in the gas have less kinetic energy. This leads to a decrease in the average speed of the particles and a narrower distribution of speeds. As a result, the peak of the curve shifts backward, indicating a lower most probable speed.
Reason behind the shift:
The shift in the peak of the curve occurs because the temperature affects the average kinetic energy of the particles. The average kinetic energy is directly proportional to the square of the speed of the particles. So, when the temperature increases, the average kinetic energy and hence the average speed of the particles increase. This leads to a shift in the peak of the curve towards higher speeds.
Additionally, the overall distribution becomes broader as the temperature increases because there is a wider range of speeds at higher temperatures. Similarly, as the temperature decreases, the overall distribution becomes narrower due to a smaller range of speeds.
Therefore, the correct answer is option 'B': Shifts forward and downward.
The Maxwell-Boltzmann distribution graph represents the distribution of speeds of particles in a gas at a given temperature. The graph is a smooth, bell-shaped curve, with the peak of the curve representing the most probable speed of the particles.
When the temperature of the gas increases, the peak of the curve shifts forward and downward. This means that the most probable speed of the particles increases, but the overall distribution becomes broader.
Effect of temperature on the shape of the curve:
- Higher temperature: At higher temperatures, the particles in the gas have more kinetic energy. This leads to an increase in the average speed of the particles and a broader distribution of speeds. As a result, the peak of the curve shifts forward, indicating a higher most probable speed.
- Lower temperature: At lower temperatures, the particles in the gas have less kinetic energy. This leads to a decrease in the average speed of the particles and a narrower distribution of speeds. As a result, the peak of the curve shifts backward, indicating a lower most probable speed.
Reason behind the shift:
The shift in the peak of the curve occurs because the temperature affects the average kinetic energy of the particles. The average kinetic energy is directly proportional to the square of the speed of the particles. So, when the temperature increases, the average kinetic energy and hence the average speed of the particles increase. This leads to a shift in the peak of the curve towards higher speeds.
Additionally, the overall distribution becomes broader as the temperature increases because there is a wider range of speeds at higher temperatures. Similarly, as the temperature decreases, the overall distribution becomes narrower due to a smaller range of speeds.
Therefore, the correct answer is option 'B': Shifts forward and downward.
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What happens to the peak of the curve in the Maxwell-Boltzmann distribution graph if temperature increases?a)Shifts forward and upwardb)Shifts forward and downwardc)Shifts backward and upwardd)Shifts backward and downwardCorrect answer is option 'B'. Can you explain this answer?
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