Define mean free path. | Physics

KINEMATIC THEORY

Very Short Question Answers

Q1. Define mean free path.
Ans.

The average distance an atom or a molecule can travel without colliding is called mean free path.

Q2. How does kinetic theory justify Avogadro's hypothesis and show than Avogadro Number in different gases is same?
Ans.

$\\ \mathbf{ \:\:\: \frac{P_1V_1}{N_1T_1}= \frac{P_2V_2}{N_2T_2}= k_B \:\: ( Boltzmann \:constant)}$

When pressure (P), volume (V) and temperature (T) remains same, the number of molecules N= constant. Hence, “equal volumes of all gases under similar conditions of temperature and pressure have the same number of molecules”. This is Avogadro’s hypothesis. kinetic theory justify Avogadro’s hypothesis.

Q3. When does a real gas behave like an
Ans.

At low pressures and high temperatures real gases behave like an ideal gases.

Q4. State Boyle's Law and Charles Law ideal gas?
Ans.

Boyle’s law: At constant temperature, the volume (v) of a given mass of a gas is inversely proportional to its pressure (P).
$\\ \mathbf{V\propto \frac{1}{P}, \:\:\: PV= constant$
Charles law: At constant pressure, the volume (v) of a given mass of a gas is directly proportional to its absolute temperature (T).

$\\ \mathbf{V\propto T, \:\:\: \frac{V}{T}= constant}$

Q5. State Dalton's law of partial pressures
Ans.

The total pressure of mixture of ideal gases is equal to the sum of the partial pressures of individual gases present in the mixture.

Total pressure (P)= P₁+P₂+P₃+...

Q6. Pressure of an ideal gas in container is independent of shape of the container-explain
Ans.

P= ⅓ mnV²The pressure depends on the mass of the gas, number of molecules in the gas and the rms velocity of the molecules. The pressure is independent of its area and volume.So pressure of an ideal gas in a container is independent of the shape of the container.

Q7. Explain the concept of degrees of freedom for molecules of a gas.
Ans.

The number of degrees of freedom of a dynamical system is defined as the total number of coordinates or independent quantities to describe completely the position and configuration of the system

Q8. What is the expression between pressure and kinetic energy of a gas molecule?
Ans.

𝑃𝑉 =⅔𝐸 (p = pressure, v= volume, E= kinetic energy)

Q9. The absolute temperature of a gas is incresed 3 times. What will be the increase in rms velocity of the gas molecule?:
Ans.

$https://latex.codecogs.com/png.image?\dpi{110}\\ \mathbf{\frac{V_{rms_1}}{V_{rms_2}}= \sqrt{\frac{T_1}{T_2}}} \Rightarrow \mathbf{V_{rms_2}= V_{rms_1}\sqrt{3}} \\ \therefore increase\:in\: the\:rms\: velocity \:\: \mathbf{V_{rms_2}-V_{rms_1}=\sqrt{3}-1=0.732}$

Short Question Answers

Q1. Explain the kinetic interpretation of Temperature

Ans. KINEMATIC THEORY

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?

Ans. KINEMATIC THEORY

Q3. Explain the concept of absolute zero of temperature on the basis of kinetic theory.

Ans. KINEMATIC THEORY

Q4. Prove that the average kinetic energy of a molecule of an ideal gas is directly proportinal to the absolute temperature of the gas.

Ans. KINEMATIC THEORY

Q5. Two thermally insulated vessels 1 and 2 of volumes V, and V are joined with a valve and filled with air at temperatures (T,. T) and presures (PP) reaspectively. If the valve joining the two vessels is opened, what will be the temperture inside the vessels at equilibrium.

Ans. KINEMATIC THEORY

Q6. What is the ratio of r.m.s speed of Oxygen and Hydrogen molecules at the same temperature?

Ans. KINEMATIC THEORY

Q7. Four molecules of a gas have speeds 1,2,3 and 4 km/s.Find the rms speed of the molecule.

Ans. KINEMATIC THEORY

Q8. If a gas has 'T degrees of freedom, find the ratio of C and C

Ans. KINEMATIC THEORY

Q9. Calculate the molecular K.E of 1 gram of Helium (Molecular weight 4) at 127°C. Given R 8.31 J mol K

Ans. KINEMATIC THEORY

Q10. When pressure increases by 2 %, what is the percentage decrease in the volume of a gas, assuming Boyle's law is obeyed?

Ans. KINEMATIC THEORY

Essay Question Answers

Q1. Derive an expression for the Pressure of an ideal gas in a container from Kinetic Theory and hence give Kinetic Interpretation of Temperature.

Ans. KINEMATIC THEORY