Question

A baloon blown up with $1$ mole of gas has a volume of $480mL$ at $5^{o}C.$ the balloon is field to $\left(7/8\right)th$ of its maximum capacity suggest. The minimum temperature at which it will brust?

• A. ${31.4}^{o}C$
• B. ${44.7}^{o}C$
• C. ${49.1}^{o}C$
• D. ${37.6}^{o}C$

Answer 1

Answer: (B)

${44.7}^{o}C$

Given,

$n_1=1$ mole

$R=0.0821$

$T_1=5^{o}C=278K$

$V_1=480ml=0.48L$

$P_1=\frac{n_{1}R{T}_1}{V_1}=\frac{1\times 0.0821\times 278}{0.48}$

$\Rightarrow P_1=47.55atm$

Now, as the given volume i.e. $480ml$ is $7/8^{th}$ of the total capacity.

Thus total volume will be

$\Rightarrow 480ml\times \frac{8}{7}=548.57ml$

The new temperature at which the balloon can burst will be at highest volume of balloon,

$P_1{V}_2=n_{1}R{T}_2$

$\Rightarrow 47.55atm\times 548.57ml=1\times 0.0821\times T_2$

$\Rightarrow T_2=317.7K$

$\Rightarrow T_2={44.7}^{o}C$

This is the minimum temperature at which balloon burst.