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Question

A glass vessel measures exactly 10 cm × 10 cm × 10 cm at 0 C. It is filled completely with mercury at this temperature. When the temperature is raised to 10 C, 1.6 cm3 of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass =6.5×106 C1.

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Solution

Vg=10×10×10=100 cc.

ΔT=10C

VHgVg=1.6 cm3

αg=6.5×106/C

γHg=?

γg=3×6.5×106/C

VHg=VHg (1+γHg ΔT) . . . (1)

Vg=Vg(1+γg ΔT) . . . (2)

VHgVg=VHgVg+VHg γHg ΔTVg γg ΔT

1.6=1000×γHg×101000×6.5×3×106×10

γHg=1.6+19.5×10210000

=1.6+0.19510000=1.79510000

=1.795×104

=1.8×104/ C


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