Question

A cylinder contains $2kg$ of air at a pressure of ${{10}^{5}}Pa$. If $2kg$ more air is pumped into it, keeping the temperature constant, the pressure will be given as,
$\begin{aligned} & A{{.10}^{10}}Pa \\\ & B.2\times {{10}^{5}}Pa \\\ & C{{.10}^{5}}Pa \\\ & D.0.5\times {{10}^{5}}Pa \\\ \end{aligned}$

Answer 1

Here the pressure and volume is said to be constant.
That is $\dfrac{P}{n}$ a constant.
The number of moles is to be found after that which is by dividing mass of air by the molecular weight of water. Then compare both the conditions and rearrange the equation. These all may help you to solve the question.
Where $n$ be the number of moles. As the volume is said to be constant, the number of moles in that specific volume at a particular pressure and temperature will be constant.

Complete answer:
First of all let us mention what all are given in the question.
The total mass of air pumped into the cylinder is given as,
$m=2+2=4kg$
The pressure at the initial stage when the mass of the air is $2kg$ can be written as,
$P={{10}^{5}}Pa$
As the temperature and the volume is a constant, we can write that,
$\dfrac{P}{n}=\text{constant}$
That means,
$\dfrac{P}{n}=\dfrac{P}{m}$
The number of moles is given as,
$n=\dfrac{\text{mass of air}}{\text{molecular weight of water}}$
Therefore we can compare both the condition now as the pressure and volume is constant.
$\dfrac{{{10}^{5}}}{2}=\dfrac{P}{\left( 2+2 \right)}$
Rearranging the equation will give the value of pressure,
$P=2\times {{10}^{5}}Pa$
Therefore the correct answer for the question has been obtained.

The correct answer is given as option B.

Note:
Basically there are four gas laws in nature. They are Boyle’s law, Charles law, Avogadro’s law and the Gay Lussac’s law. Boyle’s law says that the pressure of a certain mass of an ideal gas is inversely proportional to its volume at a fixed temperature. Charles law says that at fixed pressure the volume is directly proportional to the temperature in kelvin. The Avogadro’s law says that if the volume of the gas is equal, then the number of molecules in it will also be equal at constant temperature and pressure. Gay lussac’s law says that at constant volume, the pressure varies proportional to the temperature of the gas.