A bakelite beaker has a volume capacity of 500 cc at 30 °C. When it is partially filled with Vₘ volume (at 30 °C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If γ_b=6×10⁻⁶ °C⁻¹ and γₘ=1.5×10⁻⁴ °C⁻¹, where γ is the coefficient of volume e…

Question

A bakelite beaker has a volume capacity of 500 cc at 30 °C. When it is partially filled with Vₘ volume (at 30 °C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If γ_b=6×10⁻⁶ °C⁻¹ and γₘ=1.5×10⁻⁴ °C⁻¹, where γ is the coefficient of volume expansion, then Vₘ (in cc) is close to .

Accepted Answer

20. Given: beaker capacity V_b=500 cc, γ_b=6×10⁻⁶ °C⁻¹, γₘ=1.5×10⁻⁴ °C⁻¹. Idea: the unfilled volume is V_b-Vₘ; it stays constant exactly when the apparent expansion of the mercury is zero, i.e. when the mercury and the cavity gain the same volume. The cavity of the beaker expands like a solid piece of bakelite of the same size: Δ V_b=V_bγ_bΔ T. Setting VₘγₘΔ T=V_bγ_bΔ T gives Vₘ=(V_bγ_b)/(γₘ)=(500×6×10⁻⁶)/(1.5×10⁻⁴). Vₘ=(3×10⁻³)/(1.5×10⁻⁴)=20 cc.

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