A toy balloon can occupy $500 m l$ at $27^{0} C$ . The maximum stretching capacity of the balloon is three times of the volume at $27^{0} C$ . The temperature above which the balloon will burst , if pressure of the balloon does not change ?

300 K

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900 K

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625^{o} C

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225^{0} C

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Solution

The correct option is B $900 K$
solution:
we must know the following relation:
for any given gas, the volume of the gas is directly proportional to the temperature of the gas.
This relation can be represented as
$T α V$
When considering two sets of values for the temperature and pressure of the gas, this relation can be represented as

$\frac{T_{1}}{T_{2}} α \frac{V_{1}}{V_{2}}$
In the given problem, the values of these quantities are given as

$[T_{1}] = 27^{o} C$ = 300 K$

$V_{1} = 500 m l$

$V_{2}$ = maximum volume of the balloon $= 3 (500) = 1500 m l$

$T_{2} = ?$

Hence, the value of $T_{2}$ can be found as
$\frac{300}{T_{2}} = \frac{500}{1500}$

$T_{2} = 900 K$

Hence, Option B is the correct option.

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A toy balloon can occupy 500ml at 270C. The maximum stretching capacity of the balloon is three times of the volume at270C. The temperature above which the balloon will burst , if pressure of the balloon does not change ?

A toy balloon can occupy $500 m l$ at $27^{0} C$ . The maximum stretching capacity of the balloon is three times of the volume at $27^{0} C$ . The temperature above which the balloon will burst , if pressure of the balloon does not change ?