Question

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 mA and that in B is mB. 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 dP and 1.5dP respectively. Then

1) 4mA = 9mB 2) 2mA=3mB 3) 3mA=2mB 4) 9mA=3mB

Answer 1

The correct answer will be option 3) 3mA=2mB

Explanation :

Since the process is isothermal, hence T will be constant.

From the gas laws we know that,

PV = nRT

=> P = nRT/V

In container A,

dP = P₁ - P₂

=> dP = nₐRT/V - nₐRT/2V

=> dP = nₐRT/2V

=>  dP = mART/2MV .....................eqn1

In container B,

1.5dP = P₁ - P₂

=> 1.5dP = nᵇRT/V - nᵇRT/2V

=> 1.5dP = nᵇRT/2V

=>  1.5dP = mBRT/2MV .....................eqn2

dividing both the eqn we get,

1.5dP/dP = (mBRT/2MV)/mART/2MV

=> mB/mA = 1.5 = 3/2

=> 3mA = 2mB

Hence the correct answer will be option 3) 3mA=2mB