Question

The pressure required to stop the increase in volume of a copper block when it is heated from $50{}^{\circ }C$ to $70{}^{\circ }C$ . Coefficient of linear expansion of copper is $8\times {10}^{-6}/{}^{\circ }C$ and bulk modulus of elasticity $=3.6\times {10}^{11}N/m^2,$ is:

• A. $2.8\times {10}^{5}N/m^2$
• B. $1.72\times {10}^{8}N/m^2$
• C. $6.3\times {10}^{3}N/m^2$
• D. $8\times {10}^{-6}N/m^2$
• E. $1.57\times {10}^{4}N/m^2$

Answer 1

Answer: (B)

$B=\frac{Changeinpressure}{Volumestrain}=\frac{p}{\gamma (t_2-t_1)}$ $\therefore$ $p=B_{\gamma }(t_2-t_1)$ Given, $B=3.6\times {10}^{11}N/m^2,$ $\gamma =3\alpha =3\times 8\times {10}^{-6}=24\times {10}^{-6}/{}^{\circ }C$ $t_2-t_1=70-50=20{}^{\circ }C$ $\therefore$ $p=(3.6\times {10}^{11})(24\times {10}^{-6})(20)$ $=1.728\times {10}^{8}N/m^2$