A steel ball initially at a pressure of `1.0 xx 10^5 Pa` is heated from `20^0 C` to `120^0 C` keeping its volume constant. Find the pressure inside the ball. Coefficient of linear expansion of steel `= 12 xx 10^(-6) ^0 C^(-1)` and bulk modulus of steel `= 1.6 xx 10^(11) N m^(-2)`

Explanation

The ball tries to expand its volume but it
is kept at a constant volume.
So the stress arises
` P/((Delta V)/V) = B`
` P=B((Delta V)/(V))=B xx gamma Delta theta`
`= B xx (3 alpha Delta theta)`
`= 1.6 xx 10^11 xx 3 xx 12
xx 10^-6 xx (120-20)`
` =1.6 xx 3 xx 12 xx (10^11) xx (10^-6) xx (10^2)`
` 57.6 xx 10^7=5.8 xx 10^8 pa`