Question

The length of a soild of a metallic cube at 20°C is 5•0cm. Given that the linear expansivity of the metal is 4×^-5k^-1. Find the volume of the cube at 120°C. Find the volume of the cube at 120°C

Answer 1

Step-by-step explanation:

Length of one side of cube = 5 x 10⁻² m .

volume = ( 5 x 10⁻² )³

= 125 x 10⁻⁶ m³

Expression for thermal volume expansion is as follows :

V₂ = V₁ ( 1 + γ Δt )

V₂ and V₁ are volume before and after rise in temperature , γ is coefficient of volume expansion Δt is increase in temperature .

linear expansivity = 4 x 10⁻⁵ K⁻¹

coefficient of volume expansion γ = 3 x 4 x 10⁻⁵

= 12 x 10⁻⁵ K⁻¹

Putting the value

V₂ = 125 x 10⁻⁶ ( 1 + 12 x 10⁻⁵ x 100 )

= 125 x 10⁻⁶ + 125 x 10⁻⁶ x 12 x 10⁻³

= 125 x 10⁻⁶ + 1.5 x 10⁻⁶

= 126.5 x 10⁻⁶

= 126.5 cm³