Relation between boltsmann/gas constant and temperature

• negative
In summary, In an ideal gas, each molecule experiences a force due to the wall. The equation PV=nRT is true for an ideal gas, but the method used to calculate boltsmann constant assumes that each molecule is deflected in the opposite direction of its own. There is no evidence to support the constant multiplications of the relation between boltsmann constant and average kinetic energy of a molecule in an ideal gas.
negative
so i have been trying to calculate boltsmann constant by assuming the fact that for an ideal gas the equation :
PV=nRT is true.
i assume that for containing each molecule the wall needs to apply a force. now here is where it get's a little weird.
each molocule should be only deflected in the direction that the wall is hitting it and so each molecule hits all walls (expect the one that exactly moves parallel to the wall) and each one has effect on the pressure.
but from what i see in books, my way only works, if i assume that each molecule gets deflected exactly in opposite of it's own direction, so only one third of the molecules interact with the selected wall.
my question is that is there any sort of "evidence" that shows proves the constant multiplications of the relation between boltsmann constant and average kinetic energy of a molecule in an ideal gas which is
E=(3/2)kT ?
is there any evidence for that (3/2) or it's just purely theoretical?

About the number 3/2, you can calculate it if you've learned Statistical Mechanics course
Actually, I knew that E=(3/2)kT when I study Thermodynamics course, but we just admitted, I didn't know why we have it, until I studied Stat. mechanics

Nguyen Son said:
About the number 3/2, you can calculate it if you've learned Statistical Mechanics course
Actually, I knew that E=(3/2)kT when I study Thermodynamics course, but we just admitted, I didn't know why we have it, until I studied Stat. mechanics
well , it is highly likely that i don't know what i am talking about, but statistics doesn't give stuff out of nowhere. it calculates the result based on the model that you describe for it.
i just read the meaning of the degree of freedom. i can easily understand that the degrees of freedom in the equation
Vrms2=Vx2+Vy2Vz2
are Vx,Vy and Vz .i understand easily when i try to solve it this way. i have done it before many times. including the first times without having the knowledge.
but i wanted to do it spherical. and dang. after about 24 hour of thinking i finally found out the issue of my distribution. honestly you don't need complicated sentences to understand these kind of simple distribution. it's just about learning to think the right way. which is why i don't give up. i want to learn to think the right way.
the issue of my calculations was the fact that i considered slots for molecules based on spherical coordinates and i was offering the same amount of slots for circles with different radiuses. and the result was uneven distribution.
now i know i don't know how to define even distribution in spherical coordinates. which helps me avoid mistakes

thanks for the comment though, but i never do what you do. that's why changed physics to programming. i cannot pass if i can't give up on things that i care about. i don't have much time to study physics now but when i do, i roam free.

Question 1: What is the relation between Boltzmann constant and temperature?

The Boltzmann constant, denoted by k, is a physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas. The relation between Boltzmann constant and temperature is given by the equation k = R/N, where R is the gas constant and N is the Avogadro constant.

Question 2: How is the Boltzmann constant derived?

The Boltzmann constant is derived from the ideal gas law, which relates the pressure, volume, and temperature of a gas. Through mathematical manipulation of the ideal gas law, the Boltzmann constant can be derived as a factor that relates the average kinetic energy of particles in a gas to the temperature of the gas.

Question 3: What are the units of the Boltzmann constant?

The Boltzmann constant has units of joules per kelvin (J/K) in the SI system of units. In other systems, such as the CGS system, it can also be expressed in ergs per kelvin (erg/K).

Question 4: How does the Boltzmann constant relate to entropy?

The Boltzmann constant is also related to entropy, which is a measure of disorder or randomness in a system. The relation is given by the equation S = k ln(W), where S is the entropy, k is the Boltzmann constant, and W is the number of microstates that a system can occupy at a given energy level. This relation is known as Boltzmann's entropy formula.

Question 5: Why is the Boltzmann constant important in statistical mechanics?

The Boltzmann constant plays a crucial role in statistical mechanics, which is a branch of physics that studies the behavior of systems with a large number of particles. It is used to calculate various thermodynamic quantities, such as energy, entropy, and free energy, which are essential for understanding the behavior of gases and other systems at the molecular level.

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