# Relation between kinetic energy and temperature for hydrogen

• magodiafano
In summary, the conversation discussed the relationship between kinetic energy and temperature for hydrogen, with a question about a discrepancy between the formula given by the professor and the one found online. The summary states that the professor's notes were incorrect and that the correct formula is (3/2)KT, as seen in a derivation related to the mean kinetic energy of a particle. It is also noted that this formula is only applicable for an ideal gas.
magodiafano
Hello
I have a question about the relationship between kinetic energy and temperature for the hydrogen.

In my professor's note, there is written that:

(1/2)m*(v^2) = (1/2)*K*T

where m is the mass, K the costant and T the temperature in Kelvin.

My doubt is in the fact that on internet I discovered that the relation is:

(1/2)m*(v^2) = (3/2)*K*T

so are my professor's notes wrong?

There is a rather long, but simple derivation of the mean kinetic energy of a particle related to temperature (see http://en.wikipedia.org/wiki/Kinetic_theory). As you can see, your professor made a mistake and it is indeed (3/2)KT. Take into account however, that this is only applicable for an ideal gas.

he ain't wrong he was talking about one component of velocity

## 1. What is the relation between kinetic energy and temperature for hydrogen?

The relation between kinetic energy and temperature for hydrogen is described by the Maxwell-Boltzmann distribution, which states that the average kinetic energy of a gas is directly proportional to its temperature.

## 2. How does temperature affect the kinetic energy of hydrogen molecules?

As the temperature of a gas, such as hydrogen, increases, the average kinetic energy of its molecules also increases. This is because higher temperatures result in faster molecular motion, which leads to a greater kinetic energy.

## 3. Is there a specific formula for calculating the kinetic energy of hydrogen based on its temperature?

Yes, the kinetic energy of a gas can be calculated using the formula KE = (3/2)kT, where KE is the kinetic energy, k is the Boltzmann constant, and T is the temperature in Kelvin. This formula applies to all gases, including hydrogen.

## 4. How is the kinetic energy of hydrogen related to its internal energy?

The kinetic energy of a gas, including hydrogen, is a component of its internal energy. Internal energy also includes potential energy and the energy associated with the molecular bonds of the gas. The total internal energy of a gas is the sum of all these components.

## 5. Can the kinetic energy of hydrogen be converted to other forms of energy?

Yes, the kinetic energy of hydrogen molecules can be converted to other forms of energy, such as electrical energy, through processes like combustion or through the use of fuel cells. However, the total amount of energy in the system remains constant due to the law of conservation of energy.

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