Question

Two flasks $X$ and $Y$ have capacity 1L and 2L respectively and each of them contains 1 mole of a gas. The temperature of the flasks are so adjusted that the average speed of the molecules in $X$ is twice as that in $Y$ . The pressure in flask $X$ would be:
A. Same as that in $Y$
B. Half of that in $Y$
C. Twice of that in $Y$
D. 8 times of that in $Y$

Answer 1

Hint: The Ideal Gas Law states that the product of the pressure of a gas and volume of a gas is constant for a given sample.It is stated as follows.
$PV = nRT$ where ‘P’ is the pressure ‘V’ is the volume ‘n’ is the amount of substance ‘R’ is the ideal gas constant and ‘T’ is the temperature.

Complete step by step answer:
To understand the pressure of the flask $X$. We know that the average speed of a sample is directly proportional to the square root of temperature:
\[\dfrac{{{V_x}}}{{{V_y}}} = \dfrac{{2\sqrt {Tx} }}{{2\sqrt {{T_y}} }}\]
As given from the question
\[2 = \dfrac{{2\sqrt {{T_x}} }}{{2\sqrt {Ty} }}\]
$\Rightarrow \dfrac{{{T_x}}}{{{T_y}}} = 4$
$\Rightarrow {T_x} = 4{T_y}$
The ideal gas law states that: $PV = nRT$
If the number of moles is same
$\dfrac{{PV}}{T} \,= \,Constant$
Using it for the $X$ and $Y$ flask
\[\dfrac{{{P_x}{V_x}}}{{{T_x}}} = \dfrac{{{P_y}{V_v}}}{{{T_y}}}\]
Using the volumes as given in the question we get:
$\dfrac{{{P_x}(1)}}{{4{T_y}}} = \dfrac{{{P_y}(2)}}{{{T_y}}}$
$\Rightarrow \dfrac{{{P_x}}}{{{P_y}}} = 8$
Thus the pressure in the flask $X$ is eight times the pressure present inside the flask $Y$.

Therefore the correct option is option (D).

Note:
An ideal gas is an assumption of a real gas in which no intermolecular attractions between the molecules takes place. All the energy possessed by the gas is in the kinetic energy of the molecules of the gas and its potential energy is zero.