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

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Q. A balloon has a volume 400 ml at $0^\circ C$ . The balloon is distended to 4/5th 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?

NTA AbhyasNTA Abhyas 2020States of Matter

Solution:

(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 $^\circ C$ .