1. ⇒ (MHT CET 2023 12th May Morning Shift )

A hot air balloon has volume of $2000 {dm}^{3}$ at $99^{\circ} C$ . What is the new volume if air in balloon cools to $80^{\circ} C$ ?

A. $2428.9 {dm}^{3}$

B. $2656.9 {dm}^{3}$

C. $2814.9 {dm}^{3}$

D. $1897.8 {dm}^{3}$

Correct Option is (D)

$\begin{array}{ll} Using Charles' law, \\ \frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}} \\ ∴ & \frac{2000 {dm}^{3}}{372 K} = \frac{V_{2}}{353 K} \\ ∴ & V_{2} = \frac{2000 \times 353}{372} = 1897.8 {dm}^{3} \end{array}$

According to Charles' law, at constant pressure, the volume of a fixed mass of a gas is directly proportional to its temperature in kelvin. Therefore, as temperature decreases, volume will decrease. Hence, only option (D) is valid.

2. ⇒ (MHT CET 2023 10th May Morning Shift )

What is new temperature of a gas when its initial volume $3 {dm}^{3}$ at $300 K$ is doubled at constant pressure?

A. $450 K$

B. $600 K$

C. $750 K$

D. $900 K$

Correct Option is (B)

$\begin{array}{ll} Using Charles' law, \\ \frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}} \\ ∴ & \frac{3 {dm}^{3}}{300 K} = \frac{2 \times 3 {dm}^{3}}{T_{2}} \\ ∴ & T_{2} = \frac{2 \times 3 \times 300}{3} = 600 K \end{array}$

At constant pressure, the volume of a given amount of gas is directly proportional to its temperature in Kelvin. Therefore, if the volume doubles, the temperature will be doubled. Hence, correct answer is option (B).

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

At $0^{\circ} C$ a gas occupies 22.4 liters. What is the temperature in Kelvin to reach the volume of 224 liters?

A. $546 K$

B. $273 K$

C. $2730 K$

D. $5460 K$

Correct Option is (C)

According to Charles' law,

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$ (at constant $n$ and $P$ )

$∴ T_{2} = \frac{V_{2} \times T_{1}}{V_{1}} = \frac{224 \times 273}{22.4} = 2730 K$

⇒States of Matter