Question

Two containers $x$ and $y$ contains the same gas. If the $P,V$ and $T$ of the gas in $x$ are 2 times compared to those in $y$ and if the mass of gas in $y$ is $A$, the mass of the gas in $x$ will be:

• A. $A$
• B. $A/2$
• C. $2A$
• D. $4A$

Answer 1

The correct option is C $2A$

$PV=nRT=\frac{w}{M}RT$

$w=M\frac{PV}{RT}$

For the gas in the container $x$

$w_x=M\frac{P_x{V}_x}{R{T}_x}$......(1)

For the gas in container $y$

$w_y=M\frac{P_y{V}_y}{R{T}_y}$......(2)

Divide equation (1) by equation (2):

$\frac{w_x}{w_y}=\frac{M\frac{P_x{V}_x}{R{T}_x}}{M\frac{P_y{V}_y}{R{T}_y}}$

The $P,V$ and $T$ of the gas in $x$ are 2 times compared to those in $y$ and the mass of gas in $y$ is $A$.

$\frac{w_x}{A}=\frac{M\frac{2P_{y}2V_y}{R2T_y}}{M\frac{P_y{V}_y}{R{T}_y}}$

$w_x=2A$

Hence, the mass of the gas in $x$ will be $2A$.