A horizontal narrow glass tube of $$100$$ cm length closed at both ends contains a gas divided in to equal parts by a mercury pellet $$10$$ cm long with the system at $$127$$°C. Now one side is heated to $$227$$°C, while the other side is cooled to $$27$$°C. The distance moved by the mercury pellet in cm is nearly (neglect$$ expansion of glass and $$mercury)

Question

A horizontal narrow glass tube of $$100$$ cm length closed at both ends contains a gas divided in to equal parts by a mercury pellet $$10$$ cm long with the system at $$127$$°C. Now one side is heated to $$227$$°C, while the other side is cooled to $$27$$°C. The distance moved by the mercury pellet in cm is nearly (neglect$$ expansion of glass and $$mercury)

Infinity Learn · Accepted Answer

Initially both sides contain same number of moles and finally also they must contain same number of moles. If x is displacement of mercury pellet on the hot side the length of gas column is (45$$ $$+$$ $$x) and on the cold side it is (45$$ $$-$$ $$x). The pressures on both sides are equal and apply PV $$=$$ nTR for hot side and cold side

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