Derive an expression for the length lθ of the mercury column in a liquid-in-glass thermometer at temperature θ∘C in terms of the initial bulb volume V0 at 0∘C, the uniform capillary cross-sectional area A, the real volume expansion coefficient of mercury γm and the cubical expansion coefficient of glass γg. (Assume the length of the column at 0∘C is negligible compared with lθ.)