A vertical cylinder closed at both ends is fitted with a smooth piston dividing the volume into two parts each containing one mole of air. At the equilibrium temperature of $$320$$ K, the upper and lower parts are in the ratio $$4$$ : $$1$$. The ratio will become $$3$$ : $$1$$ at a temperature of

Question

Infinity Learn · Accepted Answer

$$p2-p1A=mgor$$                       $$mgA=RTiV1-RTi4V1=3RTi4V1$$                       …(i)Similarly$$, in second case,                          $$mgA=RTfV2-RTf3V2=2RTf3V2$$                       …$$(ii)Further$$, $$5V1$$ $$=$$ $$4V2Equating$$ Eqs. $$(i) and (ii), we get                        $$3Ti4V1=2Tf3V2$$⇒                        $$Tf=98$$×$$V2V1$$×Ti                                  $$=$$ $$98$$ × $$54$$ × $$320$$                                   $$=$$ $$450$$ K

A vertical cylinder closed at both ends is fitted with a smooth piston dividing the volume into two parts each containing one mole of air. At the equilibrium temperature of 320 K, the upper and lower parts are in the ratio 4 : 1. The ratio will become 3 : 1 at a temperature of

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