Question

A steel cylinder of $8$ liters capacity contains hydrogen gas at $12$ atm pressure. At the same temperature how many cycle tubes of $4$liters capacity at $2$ atm can be filled up with this gas?
A) \[12\]
B) \[48\]
C) \[5\]
D) \[10\]

Answer 1

Hint: We know that Boyle's law is a trial gas law that depicts how the pressure factor of a gas will in general diminish as the volume of the compartment increments.
Numerically, Boyle's law can be expressed as:
\[PV = k\]
Pressure increased by volume rises to some steady K.
Where, P is the pressure factor of the gas, V is the volume of the gas, and k is steady.

Complete answer:
The condition expresses that the result of pressure factor and volume is consistent for a given mass of kept gas and this holds as long as the temperature is steady. For contrasting similar substance under two unique arrangements of conditions, the law can be conveniently communicated as:
\[{P_1}{V_1} = {P_2}{V_2}\]
This condition shows that, as volume expands, the pressure factor of the gas diminishes in extent. Also, as volume diminishes, the pressure factor of the gas increments
\[12 \times 8 = 2 \times {V_2}\]
\[{V_2} = \dfrac{{\left( {12 \times 8} \right)}}{2}\]
On simplification we get,
\[{V_2} = 48litres\]
So we know at \[2\] ATM pressure the volume of the gas will be \[48\] liters. In any case, when the pressure factor inside and outside the chamber adjusts, no more gas is delivered. Subsequently volume equivalent to the limit of the chamber will stay back in the chamber.
Along these lines volume accessible to fill tubes = \[48liters - 8liters\]
Along these lines volume accessible to fill tubes \[ = 40liters\]
Presently for the quantity of cylinders,
Number of cylinders$ = $\[\dfrac{{40l}}{{4l}}\]
Number of cylinders \[ = 10\]
Accordingly, $10$ cylinders can be loaded up with the gas in the steel chamber.

Note:
We must know that Boyle's law is frequently utilized as a feature of a clarification on how the breathing framework functions in the human body. This usually includes clarifying how the lung volume might be expanded or diminished and along these lines cause a generally lower or higher pneumatic stress inside them. This structures a pressure factor contrast between the air inside the lungs and the ecological pneumatic force, which thus hastens either inward breath or exhalation as air moves from high to low pressure factor.