At 0^ C , a glass vessel has exact dimensions of 10 cm 10 cm 10 cm . At this temperature, the vessel is completely filled with mercury. Upon raising the temperature to 10^ C , 1.6 cm ^3 of mercury overflows. Determine the coefficient of volume expansion of mercury. The coefficient of linear expansion of glass is given as 6.5 10⁻⁶ ^ C⁻¹ .

Step-by-step solution

The initial volume of the glass vessel and mercury is V₀ = 10 10 10 = 1000 cm ^3 . The change in temperature is T = 10^ C - 0^ C = 10^ C . The coefficient of volume expansion of glass is _g = 3 _g = 3 6.5 10⁻⁶ = 19.5 10⁻⁶ ^ C ⁻¹ . The volume of mercury that overflows is given by the apparent expansion of mercury: V = V₀ _ app T Substituting the given values: 1.6 = 1000 _ app 10 _ app = 1.6 10000 = 1.6 10⁻⁴ ^ C ⁻¹ The apparent coefficient of volume expansion is related to the absolute coefficient of volume expansion