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 P and $$1.5$$ P respectively. Then

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 P and $$1.5$$ P respectively. Then

Infinity Learn · Accepted Answer

Process is isothermal. Therefore, T $$=$$ constant, (P$$ ∝ $$1V) volume is increasing, therefore pressure will decreases.In chamber A :∆P $$=$$ $$Pi-Pf$$ $$=$$ μ$$ARTV-$$μ$$ART2V$$ $$=$$ μ$$ART2V--(i)In$$ chamber B:$$1.5$$∆P $$=$$ $$Pi-Pf$$ $$=$$ μ$$BRTV-$$μ$$BRT2V$$ $$=$$ μ$$BRT2V$$   (ii)from$$ equations $$(i) and (ii)   μAμB $$=$$ $$11.5$$ $$=$$ $$23$$⇒ mAMmBM $$=$$ $$23$$ ⇒ $$3mA$$ $$=$$ $$2mB$$

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