Kinetic Theory

For molecules of a gas have speeds 1, 2, 3 and 4 km/s. The value of the root mean square speed of the gas molecules is

• $\frac{1}{2}\sqrt{15} \mathrm{km}/\mathrm{s}$

• $\frac{1}{2}\sqrt{10} \mathrm{km}/\mathrm{s}$

• 2.5 km/s

• $\frac{\sqrt{15}}{2} \mathrm{km}/\mathrm{s}$

Volume versus temperature graphs for a given mass of an ideal gas are shown in figure. At two different values of constant pressure, what can be inferred about relation between p₁ and p₂ ?

• p₁ > p₂

• p₁ = p₂

• p₁ < p₂

• data is insufficient

Determine the mean free path of argon molecules under normal condition knowing that the molecule diameter is 0.4 nm.

• 48 nm

• 60 nm

• 52 nm

• 71 nm

Six molecules speeds 2 unit, 5 unit, 3 unit, 6 units, 3 unit and 5 unit respectively. The rms speed is

• 4 unit

• 1.7 unit

• 4.2 unit

• 5 unit

At what temperature will the rms speed of air molecules be double that NTP ?

• 519° C

• 619° C

• 719° C

• 819° C

The equation of state for n moles of an ideal gas is pV = nRT, where R is a constant. The SI unit for R is

• Jk^-1 per molecule

• JK^-1 mol^-1

• JKg^-1K^-1

• Jk^-1g^-1

One mole of an ideal monoatomic gas is heated at a constant pressure from 0°C to 100°C. Then the change in the internal energy of the gas is (Given, R = 8.32 J mol^-1 K^-1)

• 0.83 × 10³ J

• 4.6 × 10³ J

• 2.08 × 10³ J

• 1.25 × 10³ J

The rms speed of oxygen is v at a particular temperature. If the temperature is doubled and oxygen molecules dissociate into oxygen atoms, the rms speed becomes

• v

• $\sqrt{2} \mathrm{v}$

• 2 v

• 4 v