Question

A balloon blown up has volume of 500ml at 5°C balloon is distended to 7/8th of its maximum capacity 1) will it burst at 30°C. 2) calculate the minimum temperature above. Which it will burst

Answer 1

Volume of balloon$=500 ml$

Volume currently filled up$(V_1)=\frac{7}{8}\times 500=437.5 ml$

Current temperature$(T_1)=5 \degree C=273+5=278 K$

$1)$ $T_2=30\degree C=273+30=303 K$

Using equation,$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

$\frac{437.5}{278}=\frac{V_2}{303}$

$V_2=\frac{437.5 \times 303}{278}=476.84ml$

So it is less than 500 ml and the balloon will not burst.

$2)$ The balloon will burst when the volume exceeds 500 ml,so the limiting case is $V_2=500 ml$

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

$\frac{437.5}{278}=\frac{500}{T_2}$

$T_2=\frac{500 \times 278}{437.5}=317.71 K$

So,the balloon will burst at temperature greater than $317.71 K \space or \space 317.71-273=44.71 \degree C$