The bulk modulus of copper is 1.4 times 10^{1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The bulk modulus $B$ is defined as $B = \frac{P}{\Delta V / V}$,where $P$ is the hydrostatic pressure.To prevent expansion,the thermal strain must

Vedclass · Accepted Answer

$7.1 	imes 10^7 \ Pa$

Vedclass · Answer

(B) The bulk modulus $B$ is defined as $B = \frac{P}{\Delta V / V}$,where $P$ is the hydrostatic pressure.To prevent expansion,the thermal strain must be balanced by the compressive strain.The thermal expansion of volume is given by $\Delta V = V \cdot 3\alpha \cdot \Delta T$,where $\alpha$ is the coefficient of linear expansion.Thus,the volumetric strain is $\frac{\Delta V}{V} = 3\alpha \Delta T$.Substituting this into the bulk modulus formula: $B = \frac{P}{3\alpha \Delta T}$.Rearranging for pressure $P$: $P = 3 B \alpha \Delta T$.Given values: $B = 1.4 	imes 10^{11} \ Pa$,$\alpha = 1.7 	imes 10^{-5} (^{\circ}C)^{-1}$,and $\Delta T = 30^{\circ}C - 20^{\circ}C = 10^{\circ}C$.Calculating $P$: $P = 3 	imes (1.4 	imes 10^{11}) 	imes (1.7 	imes 10^{-5}) 	imes 10 = 7.14 	imes 10^7 \ Pa \approx 7.1 	imes 10^7 \ Pa$.

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 $30^{\circ}C$?

Similar Questions

When the temperature of a gas is $20^{\circ} C$ and pressure is changed from $P_1 = 1.01 \times 10^5 \, Pa$ to $P_2 = 1.165 \times 10^5 \, Pa$,the volume changes by $10 \%$. The Bulk modulus is ......... $\times 10^5 \, Pa$.

The increase in pressure required to decrease the $200\,L$ volume of a liquid by $0.004\%$ in a container is ............ $kPa$. (Bulk modulus of the liquid $= 2100\,MPa$)

$A$ uniform cube is subjected to volume compression. If each side is decreased by $1\%$,then the bulk strain is

$A$ liquid of bulk modulus $k$ is compressed by applying an external pressure such that its density increases by $0.01 \%$. The pressure applied on the liquid is

Vedclass Test Series

Exam Paper Generator

Online Exam Module