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10TH GRADE · MOLECULAR KINETIC THEORY

Ideal gas and isoprocesses

Gas pressure, temperature, equation of state and gas processes.

30 minutes27 theory cards
Open interactive lesson

LESSON MATERIAL

Basic Concepts

4

Basic MKT equation

Relationship between the pressure of an ideal gas and the concentration, mass and average energy of particle motion.

Macroscopic pressure arises from the many impacts of molecules against walls; it increases when there are more particles or they move faster.

Absolute temperature

Temperature on the Kelvin scale related to the average kinetic energy of particles.

The gas laws use only kelvins: absolute temperature is directly related to the average kinetic energy of the particles.

Ideal gas equation of state

Relationship between pressure, volume, temperature and amount of substance in an equilibrium ideal gas.

For a given amount of ideal gas, the parameters p, V and T cannot be changed independently: changing two determines the third.

Isoprocess

A gas process in which one of the state parameters remains constant.

Before choosing a law, you need to determine a constant parameter: temperature, pressure or volume. The type of connection between the remaining quantities depends on this.

LESSON MATERIAL

Physical quantities

7

Mean square speed

⟨v2⟩\langle v^2\rangle

The average value of the square of the particle velocity.

Unit: square meter per square second · m2s2\frac{\mathrm{m}^2}{\mathrm{s}^2}

Average kinetic energy of a particle

⟨E⟩\langle E\rangle

Average energy of translational thermal motion of a particle.

Unit: joule · Dzh\mathrm{Dzh}

Boltzmann's constant

kk

Coefficient of connection between absolute temperature and particle energy.

Unit: joule per kelvin · DzhK\frac{\mathrm{Dzh}}{\mathrm{K}}

Absolute temperature

TT

Temperature measured on the Kelvin scale.

Unit: kelvin · K\mathrm{K}

Temperature Celsius

tt

Temperature measured on the Celsius scale.

Unit: degrees Celsius · ∘C{}^\circ\mathrm{C}

RMS speed

vkvv_{\text{kv}}

Root of the mean square of particle speed.

Unit: meter per second · ms\frac{\mathrm{m}}{\mathrm{s}}

Universal gas constant

RR

Coefficient in the equation of state of an ideal gas.

Unit: joule per mole kelvin · Dzhmol⋅K\frac{\mathrm{Dzh}}{\mathrm{mol}\cdot\mathrm{K}}

LESSON MATERIAL

Lesson formulas

16

Basic MKT equation

p=13m0n⟨v2⟩=23n⟨E⟩p=\frac{1}{3}m_0n\langle v^2\rangle=\frac{2}{3}n\langle E\rangle

Gas pressure is determined by the concentration, mass and average energy of particle motion.

Average particle energy via velocity

⟨E⟩=m0⟨v2⟩2\langle E\rangle=\frac{m_0\langle v^2\rangle}{2}

The average kinetic energy of a particle is determined by its mass and the mean square of its velocity.

Average particle energy via temperature

⟨E⟩=32kT\langle E\rangle=\frac{3}{2}kT

The average energy of translational motion of a monatomic particle is proportional to the absolute temperature.

Ideal gas pressure

p=nkTp=nkT

Pressure is equal to the product of concentration, Boltzmann's constant and absolute temperature.

Relationship between temperature scales

T=273+tT=273+t

The numerical value of temperature in Kelvin is approximately two hundred seventy-three greater than the value in Celsius.

Temperature range

1 K=1 ∘C1\,\mathrm{K}=1\,{}^\circ\mathrm{C}

A change in temperature of one kelvin is equal to a change of one degree Celsius.

RMS speed

vkv=3RTMv_{\text{kv}}=\sqrt{\frac{3RT}{M}}

The root mean square velocity of particles increases with temperature and decreases with molar mass.

Clapeyron-Mendeleev equation

pV=mMRTpV=\frac{m}{M}RT

The product of pressure and volume is determined by the amount of substance and temperature.

Equation of state through density

pM=ρRTpM=\rho RT

The pressure, molar mass, density and temperature of an ideal gas are related by one equation.

Gas density through particles

ρ=mV=m0n\rho=\frac{m}{V}=m_0n

The density of a gas is equal to the mass times the volume and the product of the mass of the particle and the concentration.

United Gas Law

pVT=const\frac{pV}{T}=\mathrm{const}

For a constant quantity of an ideal gas, the ratio of the product of pressure and volume to temperature is constant.

Boyle-Mariotte law

pV=constpV=\mathrm{const}

At constant temperature, the product of pressure and volume is constant.

Condition: The temperature and amount of gas are constant.

Charles's Law

pT=const\frac{p}{T}=\mathrm{const}

At constant volume, the ratio of pressure to absolute temperature is constant.

Condition: The volume and quantity of gas are constant.

Gay-Lussac's Law

VT=const\frac{V}{T}=\mathrm{const}

At constant pressure, the ratio of volume to absolute temperature is constant.

Condition: The pressure and quantity of gas are constant.

Boltzmann's constant

k=1,38⋅10−23 DzhKk=1{,}38\cdot10^{-23}\,\frac{\mathrm{Dzh}}{\mathrm{K}}

Boltzmann's constant relates temperature to the energy of an individual particle.

Universal gas constant

R=8,31 Dzhmol⋅KR=8{,}31\,\frac{\mathrm{Dzh}}{\mathrm{mol}\cdot\mathrm{K}}

The universal gas constant relates the macroscopic parameters of an ideal gas.

DIRECTORY

Related formulas

Speedv · m/sTemperatureT, t · K, °C

PRACTICE

Tasks on the topic

Molecular kinetic theory10 class · 12 problems