Kinetic Theory quiz

The average kinetic energy of a gas molecule is proportional to:

The rms speed of gas molecules is proportional to:

The value of gamma for a monatomic gas is:

The degrees of freedom of a diatomic molecule at moderate temperatures are:

Boyle's law holds when:

Boltzmann's constant is equal to:

If the pressure of a gas increases at constant temperature, its mean free path:

Equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules. This is:

For an ideal gas, Cp - Cv is equal to:

The energy associated with each degree of freedom per molecule is:

Why do gases deviate from ideal behaviour at high pressure and low temperature? (2 marks)

State Dalton's law of partial pressures. (2 marks)

Explain the kinetic interpretation of temperature. (2 marks)

Why is Cp greater than Cv for a gas? (2 marks)

Find the rms speed of nitrogen molecules at 300 K, taking M = 0.028 kg/mol. (2 marks)

State two assumptions of the kinetic theory of gases. (2 marks)

Using equipartition, find the molar specific heat of a solid. (2 marks)

Why does the mean free path decrease when the number density of a gas increases? (2 marks)

A car tyre is at 2 atm at 27 degrees Celsius. Find its pressure at 57 degrees Celsius if its volume is constant. (2 marks)

How many degrees of freedom does a monatomic gas molecule have? Name them. (2 marks)

Find the rms speed of helium atoms at 300 K, taking M = 0.004 kg/mol. (3 marks)

A room of 1 m^3 contains air at 27 degrees Celsius and 1 atm. Find the number of moles and the number of molecules of air in it. (3 marks)

At what temperature is the rms speed of an argon atom equal to that of a helium atom at -20 degrees Celsius? Take the molar masses of Ar and He as 39.9 and 4.0 g/mol. (3 marks)

A vessel contains 2 mol of an ideal gas at 300 K and 2 atm. Find its volume. (3 marks)

Find the total translational kinetic energy of the molecules in 1 mol of an ideal gas at 300 K. (3 marks)

Read the passage and answer the questions. A car tyre is filled with air at 2 atm and 27 degrees Celsius. After a long drive the air inside reaches 57 degrees Celsius. The volume stays constant. (i) Which gas law applies? (ii) Find the new pressure. (iii) Why should tyre pressure be checked when the tyre is cold? (5 marks)

Read the passage and answer the questions. A balloon is filled with helium at 300 K. Helium has molar mass 0.004 kg/mol. (i) Find the rms speed of helium atoms. (ii) How does it compare with that of oxygen at the same temperature? (iii) Why does helium leak from balloons faster than air? (5 marks)

Read the passage and answer the questions. A classroom of volume 1 m^3 is at 27 degrees Celsius and 1 atm. (i) Find the number of moles of air. (ii) Find the number of molecules. (iii) What happens to the number of moles if the temperature rises at constant pressure and some air escapes? (5 marks)

Read the passage and answer the questions. A student studies the specific heats of gases using equipartition. (i) Find Cv for a diatomic gas. (ii) Find Cp for it. (iii) Find gamma for it. (5 marks)

Read the passage and answer the questions. A gas is kept in a cubical box. Its molecules collide with the walls. (i) What causes the pressure of the gas? (ii) How does the pressure change if the rms speed doubles? (iii) How does the pressure change if the number of molecules doubles at the same speed? (5 marks)

Explain the molecular nature of matter and the behaviour of gases. Derive the ideal gas equation from Boyle's and Charles' laws. (6 marks)

Derive the expression for the pressure of an ideal gas from kinetic theory and show that the average kinetic energy of a molecule is (3/2)k_B T. (6 marks)

State the law of equipartition of energy. Use it to find the specific heats of monatomic, diatomic and polyatomic gases. (6 marks)

Explain the concept of mean free path. Derive an approximate expression for it and state the factors on which it depends. (6 marks)

Explain why the specific heat of a solid is about 3R per mole, and why the specific heat of water is about 9R. (6 marks)