The coefficient of volume expansion of glycerine is 49 10⁻⁵ ~K ⁻¹ . The percentage change in its density for a 50^ C rise in temperature is

Step-by-step solution

The density of a liquid at temperature T is related to its density ₀ at initial temperature T₀ by the relation = ₀ 1 + T , where is the coefficient of volume expansion and T is the change in temperature. The change in density = - ₀ = ₀ ( 1 1 + T - 1 ) = ₀ ( 1 - 1 - T 1 + T ) = - ₀ T 1 + T . For small values of T , the expression simplifies to - ₀ T . The percentage change in density is given by | ₀ | 100 = T 100 . Given = 49 10⁻⁵ K ⁻¹ and T = 50^ C = 50 K . Percentage change = 49 10⁻⁵ 50 100 = 49 50 10⁻³ = 2450 10⁻