When a metal ball is heated through 30oC,its volume becomes 1.0018cm3. If the linear expansivity of the material of the ball is 2.0 x 10-5 K-1, calculate it...
When a metal ball is heated through 30oC,its volume becomes 1.0018cm3. If the linear expansivity of the material of the ball is 2.0 x 10-5 K-1, calculate its original volume
Answer Details
When a material is heated, it expands due to increase in temperature. The amount of expansion depends on the linear expansivity of the material which is the fractional increase in length per degree rise in temperature. Let V0 be the original volume of the ball and ΔT = 30°C be the temperature rise. Then, the new volume V after heating is given by: V = V0(1 + γΔT) where γ is the linear expansivity of the material. Substituting the given values, we have: V = 1.0018 cm3 = V0(1 + 2.0 x 10-5 x 30) Simplifying the expression, we get: V0 = V / (1 + γΔT) = 1.0018 cm3 / (1 + 2.0 x 10-5 x 30) Calculating this expression gives us: V0 = 1.0000 cm3 Therefore, the original volume of the metal ball is 1.0000 cm3. Hence, the answer is 1.0000 cm3.