Bulk modulus of copper is 1.4 × 10^{11} Pa and coefficient of linear expansion is 1.7 ×

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10-1.Thermometry, Thermal Expansion and Calorimetry

hard

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

A

$6.0 × 10^5$ $Pa$

B

$7.1 × 10^7$ $Pa$

C

$5.2 × 10^6$ $Pa$

D

$40$ $atm$

Solution

Bulk Modulus $B=\frac{\frac{F}{A}}{\frac{\Delta V}{V}}$

But $\Delta V=V \times 3 \alpha \times \delta T=3 V \alpha \Delta T$

Substituting in expression for $B$

$B=\frac{\frac{F}{A}}{\frac{3 V_{\alpha} \Delta T}{V}}=\frac{P}{3 \alpha \Delta T}$

$\Rightarrow P=3 B \alpha \Delta T=3 \times\left(1.4 \times 10^{11}\right) \times\left(1.7 \times 10^{-5}\right) \times 10=7.1 \times 10^{7} P a$

Standard 11

Physics

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