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# 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 × 10–1 °C–1.

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Solution

## Given: At 0o​C, volume of glass vessel, Vg = 10 × 10 × 10 = 1000 cc = volume of mercury, VHg Let the volume of mercury at 10°C be V'Hg and that of glass be V'g. At 10​oC, the additional volume of mercury than glass, due to heating, V'Hg – V'g = 1.6 cm3 So change in temperature, ΔT = 10°C Coefficient of linear expansion of glass, αg = 6.5 × 10–6 °C–1 Therefore, the coefficient of volume expansion of glass, γg = 3 × 6.5 × 10–6°C–1​ Let the coefficient of volume expansion of mercury be γHg. We know that V'Hg = VHg (1 + γ Hg ΔT) ...(1) V'g = Vg (1 + γg ΔT) ...(2) Subtracting (2) from (1) we get, V'Hg – V'g = VHg – Vg + VHg γHg ΔT – Vg γg ΔT (as VHg = Vg) $⇒1.6=1000×{\gamma }_{\mathrm{Hg}}×10-1000×6.5×3×{10}^{-6}×10\phantom{\rule{0ex}{0ex}}⇒{\gamma }_{\mathrm{Hg}}=\frac{1.6+19.5×{10}^{-2}}{10000}\phantom{\rule{0ex}{0ex}}⇒{\gamma }_{\mathrm{Hg}}=\frac{1.6+0.195}{10000}\phantom{\rule{0ex}{0ex}}⇒{\gamma }_{Hg}=\frac{1.795}{10000}\phantom{\rule{0ex}{0ex}}⇒{\gamma }_{Hg}=1.795×{10}^{-4}\phantom{\rule{0ex}{0ex}}⇒{\gamma }_{\mathrm{Hg}}\cong 1.8×{10}^{-4}°{\mathrm{C}}^{-1}$ Therefore, the coefficient of volume expansion of mercury is 1.8× 10–4 °C–1.  Suggest Corrections  0      Similar questions  Related Videos   Thermal Expansion
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