Boltzmann constant- temp, pressure

In summary, a sealed container holds 5 × 10^1000 atoms of neon gas with a volume of 0.15 m^3. The distribution of speeds shows a peak at 2000 m s^−1. To calculate the temperature and pressure of the gas, the equations PV=nRT and PV=NkT can be used, with the knowns being volume, number of atoms, and speed. The average kinetic energy of the neon atoms can be calculated using the equation PV = 1/3 Nm<c^2>, with the known mass of each neon atom being 3.0 amu. The position of the maximum in the energy distribution can be determined using the equation PV= NkT and
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imy786
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Homework Statement



A sealed container of volume 0.15 m^3 holds a sample of 5 × 10^1000 atoms of neon gas in equilibrium. The distribution of speeds of the neon atoms shows a peak at 2000 m s^−1.

(i) Calculate the temperature and pressure of the neon gas. (6 marks)
(ii) What is the average kinetic energy of the neon atoms? (3 marks)
(iii) What is the position of the maximum in the energy distribution? (3 marks)

(Take the mass of each neon atom to be 3.0 amu.)

Homework Equations



PV=nRT
PV= NkT

PV = 1/3 Nm<c^2>

moles = mass/molar mass

The Attempt at a Solution



(i) Calculate the temperature and pressure of the neon gas

volume 0.15 m^3
5×10^1000 atoms of neon gas
speed=2000 m s^−1.
Pressure=?
Temperature= ?

I have written the knowns and unknowns.

need some help to get this started please.
 
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  • #2
(ii) What is the average kinetic energy of the neon atoms? The average kinetic energy of the neon atoms= ?Mass of each neon atom = 3.0 amuI don't know how to get started with this one.(iii) What is the position of the maximum in the energy distribution? Position of the maximum in the energy distribution = ?I don't know how to get started with this one either.
 

FAQ: Boltzmann constant- temp, pressure

1. What is the Boltzmann constant and what is its significance in science?

The Boltzmann constant is a physical constant denoted by the symbol k. Its value is approximately 1.38 x 10^-23 joules per kelvin. It relates the average kinetic energy of particles in a gas to the temperature of the gas. It is used in various equations in thermodynamics and statistical mechanics to calculate properties such as pressure, volume, and temperature of a gas.

2. How is the Boltzmann constant related to temperature and pressure?

The Boltzmann constant relates the average kinetic energy of particles in a gas to the temperature of the gas through the equation E = kT, where E is the energy, k is the Boltzmann constant, and T is the temperature. It is also used in the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

3. What are the different units for the Boltzmann constant?

The Boltzmann constant has units of joules per kelvin (J/K) in the International System of Units (SI). In other systems of units, it can also be expressed in terms of energy divided by temperature, such as ergs per kelvin (erg/K) in the centimeter-gram-second (CGS) system.

4. How is the Boltzmann constant experimentally determined?

The Boltzmann constant can be determined experimentally by measuring the speed of particles in a gas, such as in Brownian motion experiments, and relating it to the temperature of the gas. It can also be calculated using other physical constants, such as the Avogadro constant and the gas constant, through the equation k = R/NA, where NA is the Avogadro constant.

5. How does the Boltzmann constant relate to the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of a closed system will always increase over time. The Boltzmann constant is an important factor in the calculation of entropy, as it relates the number of microstates (possible arrangements of particles) to the macroscopic properties of a system. It is used to calculate the entropy of a system through the equation S = k ln(W), where S is the entropy, k is the Boltzmann constant, and W is the number of microstates.

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