Study Material
KINETIC THEORY
Very Short Answer Questions
Q1. Define mean free path and write its equation.
Q2. How does kinetic theory justify Avogadro's hypothesis?
Q3. When does a real gas behave like an ideal gas?
Q4. State Boyle's Law and Charles Law.
Q5. Pressure of an ideal gas in container is independent of shape of the container-explain.
Q6. State Dalton's law of partial pressures.
Q7. Write the equation relating pressure and internal energy.
Q8. Write the relation between pressure and kinetic energy of gas molecules.
Q9. Define rms speed of gas molecules.
Q10. The absolute temperature of a gas is increased 3 times. What will be the increase in rms velocity of the gas molecule?
Q11. Define specific heat capacity of water.
Q12. State the law of equipartition of energy.
Q13. Explain the concept of degrees of freedom for molecules of a gas.
Q14. Obtain the specific heat at constant volume for the monatomic gas.
Q15. Determine the temperature at which the rms velocity of a gas doubles its value at S. T. P. (standard temperature \(T=273\,\mathrm{K}\)).
Q16. If the temperature of an ideal gas increases from 100 K to 10000 K at constant pressure. Then find the ratio of rms speeds of the gas molecules.
Q17. Calculate the average value of energy of a molecule at a temperature of \(27^\circ\mathrm{C}\) when a gas is in thermal equilibrium. (Given \(K_B=1.38\times10^{-23}\,\mathrm{J/K}\))
Q1. Explain the kinetic interpretation of Temperature.
Q2. How specific heat capacity of mono atomic, diatomic and poly atomic gases can be explained on the basis of Law of equipartition of Energy?
Q3. Explain the concept of absolute zero of temperature on the basis of kinetic theory.
Q4. Prove that the average kinetic energy of a molecule of an ideal gas is directly proportional to the absolute temperature of the gas.
Q5. What is the ratio of rms speed of Oxygen and Hydrogen molecules at the same temperature?
Q6. Four molecules of a gas have speeds 1, 2, 3 and 4 km/s. Find rms speed of the gas molecule.
Q7. If a gas has 'f' degrees of freedom. find the ratio of \(C_p\) and \(C_v\).
Q8. Calculate the molecular K.E of 1 gram of Helium (Molecular weight 4) at \(127^\circ\mathrm{C}\). Given \(R=8.31\,\mathrm{J\,mol^{-1}K^{-1}}\).
Q9. When pressure increases by 2%, what is the percentage decrease in the volume of a gas, assuming Boyle's law is obeyed?
Q10. Determine the mean free path of a water molecule in water vapor at \(373\,\mathrm{K}\) by considering diameter (d) as \(3\times10^{-10}\,\mathrm{m}\) and number density (n) as \(2\times10^{25}\,\mathrm{m^{-3}}\).
Q1. Derive an expression for the Pressure of an ideal gas in a container from Kinetic Theory and hence give Kinetic Interpretation of Temperature.
Q1. The density of water is \(1000\,\mathrm{kg\,m^{-3}}\). The density of water vapour at \(100^\circ\mathrm{C}\) and \(1\) atm pressure is \(0.6\,\mathrm{kg\,m^{-3}}\). The volume of a molecule multiplied by the total number gives what is called molecular volume. Estimate the ratio (or fraction) of molecular volume occupied by the water vapour to the total volume occupied by the water vapour under the above conditions.
Q2. Estimate the volume of a water molecule using the data in Example 13.1.
Q3. What is the average distance between atoms (interatomic distance) in water? Use the data given in Examples 13.1 and 13.2.
Q4. A vessel contains two non-reactive gases: neon (monatomic) and oxygen (diatomic). The ratio of their partial pressures is \(3:2\). Estimate the ratio of (i) number of molecules and (ii) mass density of neon and oxygen in the vessel. Atomic mass of Ne \(=20.2\,u\), molecular mass of \(O_2=32.0\,u\).
Q5. A flask contains argon and chlorine in the ratio of \(2:1\) by mass. The temperature of the mixture is \(27^\circ\mathrm{C}\). Obtain the ratio of (i) average kinetic energy per molecule and (ii) root mean square speed \(v_{\mathrm{rms}}\) of the molecules of the two gases. Atomic mass of argon \(=39.9\,u\); molecular mass of chlorine \(=70.9\,u\).
Q6. Uranium has two isotopes of masses 235 and 238 units. If both are present in Uranium hexafluoride gas which would have the larger average speed? If atomic mass of fluorine is 19 units, estimate the percentage difference in speeds, at any temperature.
Q7. (a) When a molecule (or an elastic ball) hits a massive wall, it rebounds with the same speed. When a ball hits a massive bat held firmly, the same thing happens. However, when the bat is moving towards the ball, the ball rebounds with a different speed. Does the ball move faster or slower?\n(b) When gas in a cylinder is compressed by pushing a piston, its temperature rises. Guess an explanation for this in terms of kinetic theory using (a) above.\n(c) What happens when a compressed gas pushes a piston out and expands. What would you observe?\n(d) Sachin Tendulkar uses a heavy cricket bat while playing. Does it help him in any way?
Q8. A cylinder of fixed capacity \(44.8\) litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by \(15.0^\circ\mathrm{C}\)? \((R=8.31\,\mathrm{J\,mol^{-1}K^{-1}})\).
Q9. Estimate the mean free path for a water molecule in water vapour at \(373\,\mathrm{K}\). Use information from Exercises 13.1 and Eq. (13.41) above.