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–1 and bulk modulus of steel = 1.6 × 1011 Nm–2.

Answer 1

The pressure inside the ball $P=5.8 \times 108 P a$ at constant volume.

Explanation:

Step 1:

The steel ball Initial pressure =$1.0 \times 10^{5} \mathrm{Pa}$

The ball is heated to between 20 ° C and 120 ° C.

Change in temp, Δθ = 100 °C.

Steel  coefficient of linear expansion , $\alpha=12 \times 10^{-6} \mathrm{C}^{-1}$

Steel  Bulk modulus, $B=1.6 \times 10^{11} \mathrm{Nm}^{-2}$

Step 2:

As we know that

$P=B \times \gamma \Delta \theta$

$P=B \times 3 \alpha \Delta \theta$

$\because \gamma=3 \alpha$

$P=1.6 \times 10^{11} \times 3 \times 12 \times 10^{-6} \times(120-20)$

   $=1.6 \times 3 \times 12 \times 10^{11} \times 10^{-6} \times 100$

   $=57.6 \times 107$

$P=5.8 \times 108 P a$

So the pressure inside the ball $P=5.8 \times 108 P a$