A steel ball initially at a pressure of 1.0 ×10⁵ Pa is heated from²0°C to 120°C keeping its volume constant. Find the pressure inside the ball. Coefficient of linear expansion of steel = 12 ×10⁻⁶/°C and bulk modulus of steel = 1.6 ×10¹¹ N m⁻².
Physics · Thermodynamics
JEE Advanced

Question

A steel ball initially at a pressure of 1.0 ×10⁵ Pa is heated from²0°C to 120°C keeping its volume constant. Find the pressure inside the ball. Coefficient of linear expansion of steel = 12 ×10⁻⁶/°C and bulk modulus of steel = 1.6 ×10¹¹ N m⁻².

Physics · Thermodynamics

G1 Physics · Accepted Answer

Use ΔL=αLΔT, ΔA≈2αAΔT and ΔV≈3αVΔT (or the given cubical coefficient γ). For constrained bodies include the elastic stress needed to cancel free expansion. Substituting the given values gives 580000000.0.