Question

The bulk modulus of copper is $1.4\times {10}^{11}Pa$ and the coefficient of linear expansion is $1.7\times {10}^{-5}{(}^{\circ }C{)}^{-1}.$ 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 $7.1\times {10}^{7}Pa$

The increase in volume due to heating is
$△V_1=V_0\gamma \Delta T=V_0\left(3\alpha \right)(30-20)(\because \gamma =3\alpha )=30V_0\times 1.7\times {10}^{-5}=51V_0\times {10}^{-5}$

The decrease in volume due to pressure is,
$\Delta P=B\frac{\Delta V_2}{V_0}\Rightarrow \Delta V_2=\frac{\Delta P{V}_0}{B}$

Since there is no net change in volume,
$\Delta V_1=\Delta V_{2}51V_0\times {10}^{-5}=\frac{\Delta P{V}_0}{1.4\times {10}^{11}}\Rightarrow △P=7.14\times {10}^{7}Pa.$