Temperature

A steel ball initially at a temperature of 100kPa is heated from 20degree celcius to 120degree celcius keeping the volume constant. Find the pressure inside the ball. Coefficient of linear expansion of steel is 12*10^(-6) and the bulk modulus of steel is 1.6*10^(11)N/m2.

2 Answers

1
satan92 ·

let the initial temp be T1 and final be T2
let intial pressure be P1 and final be P2

(one thing volume cannot be kept constant it will expand(very little))
let coefficient of linear expansion =α
then coefficent of volumetric expansion=3α

hence the volume of the object changes from V to V(1+3αdT)

hence dV=3αVdT

hence B=-VdP/dV

hence dP=-BdV/V=-B*3αVdT/V=-B*3αdT=-B*3α(T2-T1)

hence P2-P1=B*3α(T1-T2)

hence we can find P2 as B,α,P1,T1,T2 are all known!!

1
Rohan Ghosh ·

good work satan :)

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