Question

A balloon has a volume $400\,ml$ at $0^\circ C$ . The balloon is distended to $4/5^{th}$ of its maximum stretching capacity.
(i) Will burst if it is brought into a room at $40^\circ C$ ?
(ii) What is the maximum temperature above which it will burst?

• A. Balloon will not burst at $40^\circ C$ , balloon will burst above $40^\circ C$
• B. Balloon will burst at $40^\circ C$ , balloon will not burst above $68.25^\circ C$
• C. Balloon will not burst at $40^\circ C$ , balloon will burst above $68.25^\circ C$
• D. None of these

Answer 1

Answer: (C)

(i) Maximum stretching capacity $=400\times \frac{5}{4}=500\, ml$
$\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}$
or $\frac{400}{273}=\frac{V_{2}}{313}$
$V_{2}=458.61\, ml$
If the volume becomes more than $500\, ml$ it will burst. The volume is below $500\, ml$, hence it will not burst at $40 ^\circ C$ .
(ii) $\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}$
or $\frac{400}{273}=\frac{500}{T_{2}}$
$T_{2}=341.25\, K = 68.25 ^\circ C$
The temperature at which the volume becomes $500\, ml$ the balloon will burst. So balloon burst above $68.26 ^\circ C$ .