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Question

A glass vessel measures exactly 10cm×10cm×10cm at 0oC. It is filled completely with mercury at this temperature. When the temperature is raised to 10oC, 1.6cm3 of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass =6.5×106 oC1.

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Solution

V0=10×10×10=1000cc

ΔT=10oC, VHGVg=1.6cm3

αg=6.5×105/oC, γHg=?, γg=3×6.5×106/oC

VHg=VHG(1+γHgΔT) ...(1)

Vg=Vg(1+γgΔT) ...(2)

VHgVg=VHgVg+VHgγHgΔTVgγgΔT

1.6=1000×γHg×101000×6.5×3×106×10

γHg=1.6+6.3×3×10210000=1.789×1041.8×104/oC

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