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Question
A steel ball that is initially at a pressure of 1.0 × 105 Pa is heated from 20°C to 120°C, keeping its volume constant.
Find the pressure inside the ball. Coefficient of linear expansion of steel = 12 × 10–6 °C–1and bulk modulus of steel = 1.6 × 1011 Nm–2.
Solution
Given:
Initial pressure on the steel ball = 1.0 × 105 Pa
The ball is heated from 20 °C to 120 °C.
So, change in temperature, Δθ = 100°C.
Coefficient of linear expansion of steel, α = 12 ×10-6°C-1
Bulk modulus of steel ,B = 1.6 × 1011 Nm–2
Pressure is given as,
⇒ P = B × γ Δθ
⇒ P =B × 3 αΔθ (∵ γ = 3 α )
⇒ P = 1.6 × 1011 ×3 × 12 × 10-6 ×(120-20)
=1.6 × 3 × 12 ×1011 ×10-6 ×102
= 57.6 × 107
⇒ P =5.8 × 108 Pa
Therefore, the pressure inside the ball is 5.8 × 108 Pa.
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