Question

An ideal gas filled at pressure of $2atm$ and temp of $300K$, in a balloon is kept in vacuum with in a large container wall of balloon is punctured then container temperature:
A.) Decreases
B.) increases
C.) remains constant
D.) unpredictable

Answer 1

Hint:
An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces.
The ideal gas equation is an empirical relationship among the volume, temperature, pressure and amount of gas which goes as follows:
$PV=nRT$
Where,
\[P = pressure~exerted\text{ }by\text{ }the\text{ }gas\]
$V = ~Volume\text{ }occupied\text{ }by\text{ }the\text{ }gas$
$n = No.\text{ }of\text{ }molecules\text{ }of\text{ }the\text{ }gas$
$R = Gas\text{ }constant$
$T = Temperature$

According to Boyle’s Law the absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system
Mathematically, Boyle's law can be stated as:$P\propto \dfrac{1}{V}$

Complete step by step solution:
We can acquire following information from the above given question:
Pressure exerted by the given ideal gas on the walls of the balloon: $2atm$
Temperature of the given ideal gas: $300K$
Since the amount of the ideal gas molecules are the same even after the walls of the balloon get punctured, $'n'$ will be constant.
After the walls of the balloon get punctured, the gas occupies the volume of the outside container.
As a result, the volume of the gas increases.
As per Boyles, with the increase in volume, there is a decrease in volume.
$P\propto \dfrac{1}{V}$
Now from the ideal gas equation, we can observe that:
$PV=nRT$
i.e $\dfrac{PV}{nR}=T$
Since the ‘n ‘and ‘R’ terms in the L.H.S are constant, the term ‘T’ in the R.H.S will remain constant since the increase in volume gets compensated by the decrease in pressure.
So, the correct answer is “Option C”.

Note: The other gas laws are as follows:
- Charles Law: It states a correlation between Temperature and volume assuming that pressure and amount of the gas remains constant.
According to this law, Volume of the gas is directly proportional to its temperature.
i.e $V\propto T$
- Avogadro's Law: It states a correlation between Amount of gas and volume assuming that pressure and temperature remains constant.
According to this law, Volume of the gas is directly proportional to the amount of the gas.
i.e: $V\propto n$