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Calculate the presure required to stop t...

Calculate the presure required to stop the increases in volume of a copper block when it is heated from `50^(@)` to `70^(@)C` . Coefficient of linear expansion of copper `=8.0xx10^(-6).^(@)C^(-1)` and bulk modulus of elasticity `3.6xx10^(11)Nm^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
1.72
When a block of volume V is heated through a temperature of `Delta T`, the change in volume is `Delta V= gamma V Delta T`
Where `gamma(= 3 alpha)` is the coefficient of cubical expansion
`therefore` volume strain `= (Detla V)/(V)= gamma Delta T`
Bulk modulus, `k= (p)/(Delta V//V)= (p)/(gamma Delta T)`
Pressure, `p= k gamma Delta T`
Here, `k= 3.6 xx 10^(11) Nm^(-2)`
`gamma= 3 alpha= 3 xx 8.0 xx 10^(-6) = 24 xx 10^(-6) ""^(@)C^(-1)`
`Delta T= 70- 50= 20^(@)C`
`therefore p= 3.6 xx 10^(11) xx 24 xx 10^(-6) xx 20 [ because p= k gamma Delta T]`
`= 1.728 xx 10^(8) Nm^(-2)`
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