A glass vessel has a volume of 1000 cc at 20^ C . Determine the volume of mercury that must be poured into the vessel at this temperature to ensure that the volume of the remaining space remains constant as the temperature varies. The coefficients of cubical expansion for mercury and glass are 1.8 10⁻⁴ ^ C⁻¹ and 9.0 10⁻⁶ ^ C⁻¹ , respectively.

Step-by-step solution

Let V_g be the volume of the glass vessel and V_m be the volume of mercury. The volume of the empty space is V_g - V_m . For this volume to remain constant with temperature, the change in volume of the glass vessel must be equal to the change in volume of the mercury. V_g = V_m V_g _g T = V_m _m T V_m = V_g _g _m Substituting the given values: V_m = 1000 9.0 10⁻⁶ 1.8 10⁻⁴ V_m = 1000 9 180 V_m = 1000 1 20 V_m = 50 cc