A metal ball initially at a pressure of 10^5 | vedclass

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

Question

(B) The metal ball tends to expand due to heating,but since its volume is kept constant,thermal stress is developed within the material.The bulk modul

Vedclass · Accepted Answer

$6 	imes 10^8 \ Pa$

Vedclass · Answer

(B) The metal ball tends to expand due to heating,but since its volume is kept constant,thermal stress is developed within the material.The bulk modulus $B$ is defined as $B = \frac{\Delta P}{\Delta V / V}$,where $\Delta P$ is the change in pressure.The fractional change in volume due to thermal expansion is given by $\frac{\Delta V}{V} = \gamma \Delta T$,where $\gamma$ is the coefficient of volume expansion and $\Delta T$ is the change in temperature.For a solid,$\gamma = 3\alpha$,where $\alpha$ is the coefficient of linear expansion.Given: $\alpha = 10^{-5} \ {^{\circ} C}^{-1}$,$\Delta T = 127^{\circ} C - 20^{\circ} C = 107^{\circ} C$,and $B = 2 	imes 10^{11} \ N \ m^{-2}$.Substituting these into the formula for pressure change: $\Delta P = B 	imes (3\alpha \Delta T)$.$\Delta P = (2 	imes 10^{11}) 	imes (3 	imes 10^{-5} 	imes 107) = 6 	imes 10^6 	imes 107 = 6.42 	imes 10^8 \ Pa$.The final pressure $P_f = P_i + \Delta P = 10^5 \ Pa + 6.42 	imes 10^8 \ Pa \approx 6.42 	imes 10^8 \ Pa$.Rounding to the nearest given option,the pressure becomes approximately $6 	imes 10^8 \ Pa$.

Similar Questions

$A$ metal rod having a coefficient of linear expansion $2 \times 10^{-5} /{ }^{\circ} C$ is $0.75 \ m$ long at $45^{\circ} C$. When the temperature rises to $65^{\circ} C$,the increase in length of the rod will be: (in $mm$)

When a bimetallic strip is heated, it . . . . . . .

The linear expansion coefficients of brass and steel wires are $\alpha_1$ and $\alpha_2$ respectively,and their lengths at $0^\circ C$ are $L_1$ and $L_2$. If the difference $(L_2 - L_1)$ remains constant at any temperature,then:

The coefficient of superficial expansion of a solid is $2 \times 10^{-5} \text{ °C}^{-1}$. Its coefficient of linear expansion is:

$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \,m$ at a certain temperature. The maximum temperature variation allowable during the ruling is (Coefficient of linear expansion of steel $= 10 \times 10^{-6} \,K^{-1}$) (in $^{\circ} C$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module