A piece of metal weighs 45 ~g in air and 25 ~g in a liquid of density 1.5 10^3 ~kg ⁻³ ~m ⁻³ kept at 30^ C . When the temperature of the liquid is raised to 40^ C , the metal piece weighs 27 ~g . The density of liquid at 40^ C is 1.25 10^3 ~kg - m ⁻³ . The coefficient of linear expansion of metal is

Step-by-step solution

The volume of the metal at 30^ C is aligned V₃₀ & = loss of weight specific gravity g & = (45-25) g 1.5 g =13.33 ~cm ^3 aligned Similarly, volume of metal at 40^ C is V₄₀= (45-27) g 1.25 g =14.40 ~cm ^3 Now, V₄₀=V₃₀ [1+ (t₂-t₁ ) ] aligned or & = V₄₀-V₃₀ V₃₀ (t₂-t₁ ) & = 14.40-13.33 13.33(40-30) & =8.03 10⁻³ / ^ C aligned Coefficient of linear expansion of the metal is aligned = 3 & = 8.03 10⁻³ 3 & 2.6 10⁻³ / ^ C aligned