1. ⇒ (MHT CET 2023 9th May Evening Shift )

An ideal gas in a container of volume 500 c.c. is at a pressure of $2 \times 10^{+ 5} N / m^{2}$ . The average kinetic energy of each molecule is $6 \times 10^{- 21} J$ . The number of gas molecules in the container is

A. $5 \times 10^{25}$

B. $5 \times 10^{23}$

C. $25 \times 10^{23}$

D. $2.5 \times 10^{22}$

Correct Option is (D)

$PV = {Nk}_{B} T$

and, K.E./molecule $= \frac{3}{2} k_{B} T = \frac{3}{2} \frac{PV}{N}$

$\begin{aligned} ∴ N & = \frac{3}{2} \times \frac{PV}{(K.E./molecule)} \\ = \frac{3}{2} \times \frac{2 \times 10^{5} \times 500 \times 10^{- 6}}{6 \times 10^{- 21}} = 2.5 \times 10^{22} \end{aligned}$

2. ⇒ (MHT CET 2023 9th May Morning Shift )

According to kinetic theory of gases, which one of the following statements is wrong?

A. All the molecules of a gas are identical.

B. Collisions between the molecules of a gas and that of the molecules with the walls of the container are perfectly elastic.

C. The molecules do not exert appreciable force on one another except during collision.

D. The pressure exerted by a gas is due to the collision between the molecules of the gas.

Correct Option is (D)

Currently no explanation available

3. ⇒ (MHT CET 2021 21th September Evening Shift )

If ' $E$ ' is the kinetic energy per mole of an ideal gas and ' $T$ ' is the absolute temperature, then the universal gas constant is given as

A. $\frac{2 T}{3 E}$

B. $\frac{2 E}{3 T}$

C. $\frac{3 T}{2 E}$

D. $\frac{3 E}{2 T}$

Correct Option is (B)

The kinetic energy per mole E = $\frac{3}{2}$ RT

$∴ R = \frac{2 E}{3 T}$

⇒Kinetic Theory of Gases