Question

For a given mass of a gas, if pressure is reduced to half and temperature is doubled, then the volume $V$ will become
$A.$ $4V$
$B.$ $2{V^2}$
$C.$ $V/4$
$D.$ $8V$

Answer 1

Hint:The given solution will be solved by using the ideal equation (An ideal equation is the relation between pressure, Temperature, amount of substance and volume). The ideal equation is combination of Boyle’s law, Charles’s law and Avogadro’s law

Complete step by step answer:
Let the pressure $\left( P \right)$, temperature $\left( T \right)$ and volume $\left( V \right)$.It is given that pressure is reduced to half so pressure becomes $\left( {\dfrac{P}{2}} \right)$ and temperature is double so temperature becomes $\left( {2T} \right)$.We have to calculate the change in volume $\left( {V'} \right)$ at this condition.
We know the ideal gas equation,
$PV = nRT$
$ \Rightarrow $ $V = \dfrac{{nRT}}{P}$
According to the condition when pressure is reduced to half and temperature is double, then the volume $V'$ becomes,
$V' = \dfrac{{nR\left( {2T} \right)}}{{\dfrac{P}{2}}}$
$ \Rightarrow $ $V' = \dfrac{{nRT\left( 4 \right)}}{P}$
$ \Rightarrow $ $V' = 4V$ $\left[ {\because V = \dfrac{{nRT}}{P}} \right]$

Hence, the volume becomes four times. So, the correct option is $A.$

Additional information:
Boyle’s law: It states that at constant temperature and amount of gas pressure is inversely proportional to the volume of gas.
Charles’s law: It states that at constant pressure and amount of gas volume is directly proportional to the temperature of gas.
Avogadro’s law: It states that at constant pressure and temperature the amount of gas is directly proportional to volume of gas.
Gay Lussac’s law: It states that at constant volume of gas the pressure of gas is directly proportional to its temperature.

Note:
The ideal gas law also called the general gas equation is the equation of state of a hypothetical ideal gas. The ideal gas law states that under the same temperature, pressure, and volume all gases contain the same number of molecules. The ideal gas law does not apply when the temperatures are near the point of transforming into a liquid or solid.