Question

In a cylinder, Oxygen gas is filled. It is fount that the temperature becomes four times when the pressure is doubled. Now, find the ratio of the final density and the initial density of this gas:

• A. $2$
• B. $4$
• C. $\frac{1}{4}$
• D. $\frac{1}{2}$

Answer 1

Answer: (D)

We can write ideal gas equation in a modified form as given below:-
$P{M}_w=\rho RT$
This form incorporates molecular weight, $M_w$ and density, $\rho$ .
Rearranging the equation, we get:
$\rho =\frac{M_{W}P}{RT}$ .........(i)
It is given in question that $P_2=2P,T_2=4T$
Substituting the values and calculating, we obtain:-
$\Rightarrow {\left(\rho \right)}^{{}^{\prime }}=\frac{M_W\cdot 2P}{R(4T)}\Rightarrow {\left(\rho \right)}^{{}^{\prime }}=\frac{\rho }{2}[\text{ from }(i)]$