Chapter 9 : KINETIC THEORY OF GASES

Oxygen molecules at temperature T have the same r.m.s. speed as helium molecules at 300 K. What is the temperature T ?

• 106 K

• 600 K

• 850 K

• 2400 K

The volume of an ideal gas is V when its pressure is p. The r.m.s. speed of the gas molecules is proportional to

• pV

• p/V

• √pV

• √p/V

The pressure of an ideal gas in a vessel is 1.5×10⁵ Pa when the temperature is 350 K. What is the number of gas molecules per unit volume?

• 1.7×10²⁰ m^-3

• 1.4×10²¹ m^-3

• 1.2×10²² m^-3

• 3.1×10²⁵ m^-3

The pressure of an ideal gas in a vessel is p. The gas is heated at constant volume until the r.m.s. speed of the gas molecules is doubled. what is the new pressure of the gas?

• √2p

• 2p

• 3p

• 4p

Which of the following is not an assumption of the kinetic theory of gases?

• Gas molecules move with the same speed, known as the r.m.s. speed

• Gas molecules are in constant free random motion

• Collisions between gas molecules are perfectly elastic

• The size of a gas molecule is negligible compared to the distance between gas molecules

Which statement about the internal energy U of a fixed mass of an ideal gas of pressure p, volume V and temperature T is correct?

• U ∝ p

• U ∝ pV

• U ∝ V

• U ∝ √T

The molecular speed distribution of a gas is shown in the figure above. Which of the statements is correct?

• The mean speed is V^'

• The r.m.s. speed is greater than V^'

• The maximum number of molecules is n^'

• More than half of the number of molecules have speeds less than V^'

When the pressure if air in a balloon is increased by 2% by pumping air into the balloon, it is found that the number of moles of air in the balloon has increased by 5%, the thermodynamic temperature increased by 2%. By What percentage has the volume of the balloon changed?

• Decreased by 3%

• Decreased by 5%

• Increased by 5%

• Increased by 7%

The root-mean square speed of the molecules of a gas in a closed container is v. If the gas is heated at constant volume until the pressure is doubled, what is the r.m.s. speed now?

• ^{1/2 v}

• 1/√2 v

• √2 v

• 2 v

The pressure of an ideal gas in a closed container is p, and the mean kinetic energy of the molecules is E. If the mean kinetic energy increase to 9E, what is the pressure of the gas?

• 3p

• 9p

• 27p

• 81p