Two identical containers A and B have frictionless pistons. They contain the same volume of an ideal gas at the same temperature. 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 double the initial volume. The change in the pressure in A and B, respectively, is Δp and $$1.5$$Δp. Then

Question

Two identical containers A and B have frictionless pistons. They contain the same volume of an ideal gas at the same temperature. 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 double the initial volume. The change in the pressure in A and B, respectively, is Δp and $$1.5$$Δp. Then

Infinity Learn · Accepted Answer

For the gas in container A       Δ$$P=PAfinal$$ −PAinitial $$=nART2V$$−nARTV               Δ$$P=$$−$$nART2V$$  …….(i)For$$ gas in container B         $$1.5$$Δ$$P=PBfinal$$ −PAinitial $$=nBRT2V$$−nBRTV        $$1.5$$Δ$$P=$$−$$nBRT2V$$   …….$$(ii)From$$ Eqs. $$(i) and (ii), we get          $$nB=1.5nA$$⇒ $$2nB=3nA$$⇒ $$2mB=3mA$$

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