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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. - Physics

Answer in Brief

A steel ball that is initially at a pressure of 1.0 × 10Pa 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.

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Solution

Given:
Initial pressure on the steel ball = 1.0 × 10Pa 
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 × 10Pa.

Concept: Temperature and Heat
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 1 Heat and Temperature
Q 31 | Page 14
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