Question

If the pressure becomes double at the same absolute temperature on $ 2l $ $ C{O_2} $ , then the volume of $ C{O_2} $ becomes
(A) $ 2l $
(B) $ 4l $
(C) $ 25l $
(D) $ 1l $

Answer 1

Hint :To solve this question. First we need to know the laws that govern gases and their behaviour on changing surrounding conditions. One such rule related to our question is Boyle’s law that correlates the pressure and the volume of the gas.

Complete Step By Step Answer:
Boyle’s law states that the pressure of the given quantity of gas is inversely proportional to the volume of the gas at the constant temperature.
So we can say
 $ P\alpha \dfrac{1}{V} $
 $ {P_1}{V_1} = {P_2}{V_2} $
If one entity doubles, the other decreases.
So, let’s. Solve the equation for better understanding.
Assume, Initial pressure $ {P_1} $ $ = {\text{ P}} $
Final pressure $ {P_2} = {\text{ 2P}} $
Initial volume $ {V_1} = 2V $
Final Volume $ {V_2} = ? $
Putting the values in equation
 $ {P_1}{V_1} = {P_2}{V_2} $
 $ {V_2} = \dfrac{{P \times 2V}}{{2P}} $
 $ {V_2} = 1{\text{ litre }} $ .
Thus, the answer is $ 1{\text{ litre}} $
So, if the pressure becomes double at the same absolute temperature on $ 2l $ $ C{O_2} $ , then the volume of $ C{O_2} $ becomes $ 1{\text{ litre}} $ .
Therefore, the correct answer is Option D.

Note :
There are other few laws also that govern the nature of gases on changing the environmental conditions. One such other law is Charles law. Charles law states that the volume occupied by the fixed amount of gas is directly proportional to the given temperature at the constant pressure. It means if we increase the temperature, then the volume of the gas will also increase as the particles will undergo more random motion and will result in an increase in volume. Interesting fact is that this law can be derived from the kinetic theory of gases which makes it a special law. This Charles law was given by J.A.C Charles in $ 1787 $ .