Question

The bulk modulus of copper is $1.4\times {10}^{11}Pa$ and the coefficient of linear expansion is $1.7\times {10}^{-5}(C^{\circ }{)}^{-1}$. What hydrostatic pressure is necessary to prevent a copper block from expanding when its temperature is increased from ${20}^{\circ }C$ to ${30}^{\circ }C$?

• A. $6.0\times {10}^{5}Pa$
• B. $7.1\times {10}^{7}Pa$
• C. $5.2\times {10}^{6}Pa$
• D. $40atm$

Answer 1

The correct option is B $7.1\times {10}^{7}Pa$

Bulk Modulus $B=\frac{\frac{F}{A}}{\frac{\Delta V}{V}}$
But $\Delta V=V\times 3\alpha \times \delta T=3V\alpha \Delta T$
Substituting in expression for B
$B=\frac{\frac{F}{A}}{\frac{3V\alpha \Delta T}{V}}=\frac{P}{3\alpha \Delta T}$
$\Rightarrow P=3B\alpha \Delta T=3\times (1.4\times {10}^{11})\times (1.7\times {10}^{-5})\times 10=7.1\times {10}^{7}Pa$