Two identical cylinders A and B with frictionless pistons contain the same ideal gas at same temperature and the same volume V. The mass of gas A is $m_{A}$ and that of B is $m_{B}$ . The gas in each cylinder is allowed to expand isothermally to the same final volume 2V. The change in the pressure in A and B are found to be $Δ P$ and 1.5 $Δ P$ respectively. Then

4 m_{A}

9 m_{B}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 m_{A}

3 m_{B}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 m_{A}

2 m_{B}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

9 m_{A}

4 m_{B}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $3 m_{A}$ = $2 m_{B}$
Since the process is isothermal, $T$ will be constant.

From the gas laws we know that,

$P V = n R T$

$⟹ P = \frac{n R T}{V}$

In container $A$ ,

$d P = P_{1} - P_{2}$

$⟹ d P = \frac{n_{a} R T}{V} - \frac{n_{a} R T}{2 V}$

$⟹ d P = \frac{n_{a} R T}{2 V}$

$⟹ d P = \frac{m_{A} R T}{2 M V}$ ..................... (1)

In container $B$ ,

$1.5 d P = P_{1} - P_{2}$

$⟹ 1.5 d P = \frac{n_{b} R T}{V} - \frac{n_{b} R T}{2 V}$

$⟹ 1.5 d P = \frac{n_{b} R T}{2 V}$

$⟹ 1.5 d P = \frac{m_{B} R T}{2 M V}$ ..................... (2)

Dividing both the eqn we get,

$\frac{1.5 d P}{d P} = \frac{(\frac{m_{B} R T}{2 M V})}{(\frac{m_{A} R T}{2 M V})}$

$⟹ \frac{m_{B}}{m_{A}} = 1.5 = \frac{3}{2}$

$3 m_{A} = 2 m_{B}$

Suggest Corrections

Similar questions

Q. Two identical containers A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The mass of the gas in A is

m_{A}

and that in B is

m_{B}

. The gas in each cylinder is now allowed to expand isothermally to the same final volume 2V. The changes in the pressure in A and B are found to be

△ P

and 1.5

△ P

respectively. Then

Two identical containers A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V. The mass of the gas in A is $m_{A}$ and that in B is $m_{B}$ The gas in each cylinder is now allowed to expand isothermally to the same final volume 2V. The changes in the pressure in A and B are found to be $△ P$ and 1.5 $△ P$ respectively. Then