Question

A balloon blown up with $1$ mole of a gas, has a volume of $480\text{mL}$ to $5^{\circ }C$. If the balloon is filled to $\left(\frac{7}{8}\right)th$ of its maximum capacity, then which of the following options is/are correct ?

• A. The balloon will burst at ${30}^{\circ }C$
• B. The pressure of the gas inside the balloon at $5^{\circ }C$ is 47.5 atm
• C. The minimum temperature at which the balloon will burst is ${44.71}^{\circ }C$
• D. The pressure of gas when balloon burst at minimum temperature is 50 atm

Answer 1

Answer: (B), (C)

The minimum temperature at which the balloon will burst is ${44.71}^{\circ }C$

Maximum capacity or volume of balloon $V_2=\frac{8}{7}\times 480=548.57\text{mL}$
Also, $V_1=480\text{mL},T_1=278K,n=1\text{mole}$
(A) The balloon will burst at a minimum temperature $\left(T_2\right)$ when volume becomes $548.57\text{mL}$.
Using Charle's law
$\therefore \frac{V_1}{T_1}=\frac{V_2}{T_2}$
$\frac{480}{278}=\frac{548.57}{T_2}$
$\therefore T_2={44.71}^{\circ }C$
Hence, (A) is incorrect but (C) is correct.

(B) Pressure of the gas at $5^{\circ }C$ having 1 mole and $V=480\text{mL}$
$PV=nRT$
$\therefore P\times \frac{480}{1000}=1\times 0.0821\times 278$
$\therefore P=47.5\text{atm}$
Hence, (B) is also correct.

(D) Since, $V$ increases with increase in temperature from $5^{\circ }C$ to ${44.71}^{\circ }C$, at which balloon bursts and therefore pressure remains constant. Thus pressure of gas inside the balloon when it bursts is $47.5\text{atm}$. Hence, (D) is incorrect.
Hence (B, C) are correct.