Question

A toy balloon can occupy 500ml at 27 $^\circ C$. The maximum stretching capacity of the balloon is three times the volume at 27 $^\circ C$. The temperature above which the balloon which the balloon will burst, if pressure of the balloon does not change
A. 300 K
B. 900 K
C. 625 $^\circ C$
D. 225 $^\circ C$

Answer 1

For solving this question, we must follow the following steps: first find a relation between the temperature and volume of the gas. Remember, the condition given to us is that the pressure is constant. So we won’t be needing pressure in this relationship. Then we must simply substitute the values and obtain the value for $T{}_2$

Formula used: $\dfrac{{T{}_1}}{{T{}_2}}\,\alpha \,\dfrac{{V{}_1}}{{V{}_2}}$

Complete Step-by-Step Answer:
For solving this question, we must know the following relation: for any given gas, the volume of the gas is directly proportional to the temperature of the gas. To put this in simpler words, we can say that if the value of the temperature of the gas is increasing, then the value of the volume of the gas will also increase in a linear manner. This relation can be represented as:
$T\,\alpha \,V$
When considering two sets of values for the temperature and pressure of the gas, this relation can be represented as:
$\dfrac{{T{}_1}}{{T{}_2}}\,\alpha \,\dfrac{{V{}_1}}{{V{}_2}}$
In the given problem, the values of these quantities are given as:
$T{}_1$ = 27 $^\circ C$= 300 K
$V{}_1$ = 500 ml
$V{}_2$ = maximum volume of the balloon = $3{\text{ }}\left( {500} \right){\text{ }} = {\text{ }}1500$ ml
$T{}_2$ = ?
Hence, the value of $T{}_2$ can be found as:
$\dfrac{{300}}{{T{}_2}}\, = \,\dfrac{{500}}{{1500}}$
$T{}_2$ = 900 K

Hence, Option B is the correct option.

Note: The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behaviour of many gases under many conditions, although it has several limitations. The equation for the ideal gas law can be given as:
PV = nRT
This helps us find the relations between the different physical parameters of the given gas.