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Kinetic theory of gases – problems and solutions

1. Ideal gases in a closed container initially have volume V and pressure P. If the final pressure is 4P and the volume is kept constant, what is the ratio of the initial kinetic energy with the final kinetic energy.

Known :

Initial pressure (P1) = P

Final pressure (P2) = 4P

Initial volume (V1) = V

Final volume (V2) = V

Wanted: The ratio of the initial kinetic energy with the final kinetic energy (KE1 : KE2)

Solution :

The relation between pressure (P), volume (V) and kinetic energy (KE) of ideal gases :

Kinetic theory of gases - problems and solutions 18

The ratio of the initial kinetic energy with the final kinetic energy :

Kinetic theory of gases - problems and solutions 19

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2. What is the average translational kinetic energy of molecules in an ideal gas at 57oC.

Known :

Temperature of gas (T) = 57oC + 273 = 330 Kelvin

Boltzmann‘s constant (k) = 1.38 x 10-23 Joule/Kelvin

Wanted: The average translational kinetic energy

Solution :

The relation between kinetic energy (KE) and the temperature of the gas (T) :

Kinetic theory of gases - problems and solutions 3

The average translational kinetic energy :

Kinetic theory of gases - problems and solutions 4

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3. A gas at 27oC in a closed container. If the kinetic energy of the gas increases 2 times the initial kinetic energy, thus the final temperature of the gas is…

Known :

Initial temperature (T1) = 27oC + 273 = 300 K

Initial kinetic energy = KE

Final kinetic energy = 4 KE

Wanted: The final temperature (T2)

Solution :

Kinetic theory of gases - problems and solutions 5

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4. An ideal gas is in a closed container, is heated so that the final average velocity of particles of gas increases by 3 times the initial average velocity. If the initial gas temperature is 27oC, then the final temperature of the ideal gas is…

Known :

Initial temperature = 27oC + 273 = 300 Kelvin

Initial velocity = v

Final velocity = 2v

Wanted : The final temperature of ideal gas

Solution :

Kinetic theory of gases - problems and solutions 20

The final average velocity = 2 x the initial average velocity

Kinetic theory of gases - problems and solutions 7

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5. Three moles of gas are in a 36 liters volume space. Each gas molecule has a kinetic energy of 5 x 10-21 Joule. Universal gas constant = 8.315 J/mole.K and Boltzmann’s constant = 1.38 x 10-23 J/K. What is the gas pressure in the container.

Known :

Number of moles (n) = 3 moles

Volume = 36 liters = 36 dm3 = 36 x 10-3 m3

Boltzmann’s constant (k) = 1.38 x 10-23 J/K

Kinetic energy (KE) = 5 x 10–21 Joule

Universal gas constant (R) = 8.315 J/mole.K

Wanted : Gas pressure (P)

Solution :

Calculate the temperature using the equation of kinetic energy of gas.

Kinetic theory of gases - problems and solutions 8

Calculate the gas pressure using th equation of ideal gas law (in number of moles, n) :

P V = n R T

P (36 x 10-3) = (3)(8.315)(241.5)

P (36 x 10-3) = 6024.22

Kinetic theory of gases - problems and solutions 9

The gas pressure is 1.67 x 105 Pascal or 1.67 atmospheres.

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