Two identical glass spheres filled with air are connected by a horizontal glass tube. The glass tube contains a pellet of mercury at its mid-point. Air in one sphere is at 0°C and the other is at 20°C. If both the vessels are heated through 10°C, then neglecting the expansions of the bulbs and the tube.

the mercury pellet gets displaced towards the sphere at a lower temperature.

The mercury pellet gets displaced towards the sphere at a higher temperature

The mercury pellet does not get displaced at all.

the temperature rise causes the pellet to expand with any displacement.

Solution

The mercury pellet does not get displaced at all.

Let n1 and n2 be the number of moles in the bulbs at 0°C and 20°C, respectively, then,

pV = 273n₁R = 293n₂R

$\frac{n_{1}}{n_{2}} = \frac{293}{273} . . . (i)$

when the vessels are heated, let the volume of low temperature be V₁ and that of the other be V₂. Since pressure are same, hence

V₁p = 283 n₁R and V₂p = 303 n₂R

$\frac{V_{1}}{V_{2}} = \frac{283 n_{1}}{303 n_{2}} . . . (ii)$

From Eqs. (i) and (ii), we get

$\frac{V_{1}}{V_{2}} = \frac{283}{303} x \frac{293}{273} = 1$

Thus, the mercury pellet remains at the same position.

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