# Basic Monatomic Ideal Gas Speed/Temperature Relationship

• jacksonpeeble
In summary, the speed of monatomic gas particles is directly proportional to their temperature, as stated by the kinetic theory of gases. The equation for this relationship is known as the Maxwell-Boltzmann distribution and is represented by the square root of (3RT/M), with R being the gas constant, T being the temperature in Kelvin, and M being the molar mass of the gas. Changing the temperature of a gas will directly impact the average speed of its particles, with higher temperatures resulting in faster particle movement and lower temperatures resulting in slower particle movement. However, the relationship between gas speed and temperature varies for different types of gases and is not affected by the size or shape of gas particles.
jacksonpeeble
Gold Member
What would happen to the temperature (in Kelvin) if the speed of every atom in a monatomic ideal gas were doubled (specifically, what multiplication factor would be used)?

Temperature is proportional to the kinetic energy. If the speed of every atom doubles, the temperature would rise by a factor of 4.

Thanks, that makes sense.

## 1. How is the speed of monatomic gas particles related to their temperature?

The speed of monatomic gas particles is directly proportional to their temperature. As the temperature of a gas increases, the average speed of its particles also increases. This is known as the "kinetic theory of gases."

## 2. What is the equation for the relationship between gas speed and temperature?

The equation for the relationship between gas speed and temperature is known as the "Maxwell-Boltzmann distribution." It states that the average speed of gas particles (v) is equal to the square root of (3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

## 3. How does changing the temperature of a gas affect its speed?

Changing the temperature of a gas will directly impact the average speed of its particles. As the temperature increases, the particles will move faster, and as the temperature decreases, the particles will slow down.

## 4. Is the relationship between gas speed and temperature the same for all types of gases?

No, the relationship between gas speed and temperature varies depending on the type of gas. It is different for monatomic, diatomic, and polyatomic gases, as well as for gases with different molar masses.

## 5. How does the size of gas particles affect their speed and temperature relationship?

The size of gas particles does not affect their speed and temperature relationship. This relationship is solely dependent on the temperature and molar mass of the gas particles, not their size or shape.

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