Calculate the pressure requird to stop the increase in volume of a copper block when it is heated from `60^@C` to `80^@C.` Coefficient of linear expansion of copper is `8.0 xx 10^(-6), .^@C^(-1)` and Bulk modulus of elasticity ` = 3.6 xx 10^(11) Nm^(-2)`

Answer

`1.73xx10^8 Nm^(-2)`

Explanation

Here, Delta `T = 80-60 = 20^@C = 20 K ,`
`alpha = 8.0 xx 10^(-6) , .^@C^(-1),`
`gamma = 3 alpha = 3xx 8.0 xx 10^(-6) = 24 xx 10^(-6), .^@C^(-1),`
`B = 3.6 xx 10^(11) Nm^(-2)`
Increase in volume V of a copper block when heated through a temperature `Delta T` is `Delta V = gamma V Delta t` where `gamma ( = 3 alpha)` is the coefficient of cubical expansion of copper block. Let p be the increase in pressure required to decrease the volume of block by `Delta V'` then `B = (pV)/(Delta V')` or `Delta V' = (pV)/(B)` There will be no increase in volume of the copper block if `Delta V' = Delta V` or `(pV)/(B) = gamma V Delta T`
or `p = gamma B delta T = (24xx10^(-6)xx(3.6xx10^(11))20`
` = 1.73 xx 10^8 Nm^(-2)`