When the temperature of a metal sphere is inc | vedclass

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

Question

(A) The formula for volume expansion is given by $\frac{\Delta V}{V} = \gamma \Delta 	heta$,where $\gamma$ is the coefficient of volume expansion and

Vedclass · Accepted Answer

$2 	imes 10^{-5}$

Vedclass · Answer

(A) The formula for volume expansion is given by $\frac{\Delta V}{V} = \gamma \Delta 	heta$,where $\gamma$ is the coefficient of volume expansion and $\Delta 	heta$ is the change in temperature.Given $\frac{\Delta V}{V} = 0.24\% = \frac{0.24}{100} = 2.4 	imes 10^{-3}$ and $\Delta 	heta = 40^{\circ}C$.Substituting the values: $2.4 	imes 10^{-3} = \gamma 	imes 40$.Solving for $\gamma$: $\gamma = \frac{2.4 	imes 10^{-3}}{40} = 0.06 	imes 10^{-3} = 6 	imes 10^{-5} \, ^{\circ}C^{-1}$.The relationship between the coefficient of linear expansion $(\alpha)$ and the coefficient of volume expansion $(\gamma)$ is $\alpha = \frac{\gamma}{3}$.Therefore,$\alpha = \frac{6 	imes 10^{-5}}{3} = 2 	imes 10^{-5} \, ^{\circ}C^{-1}$.

When the temperature of a metal sphere is increased by $40^{\circ}C$,its volume increases by $0.24\%$. The coefficient of linear expansion of the metal is ....... $^{\circ}C^{-1}$.

Similar Questions

$A$ steel tape is calibrated at $20^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$,the percentage error in the tape will be ........... $\%$ $\left[\alpha_{\text{steel}} = 1.2 \times 10^{-5} {}^{\circ} C^{-1}\right]$

$A$ 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 $mm$)

The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6} \, ^{\circ}C^{-1}$ and in a steel vessel is $144 \times 10^{-6} \, ^{\circ}C^{-1}$. If $\alpha$ for steel is $12 \times 10^{-6} \, ^{\circ}C^{-1}$,then that of glass is:

An iron bar of length $10\, m$ is heated from $0^{\circ}C$ to $100^{\circ}C$. If the coefficient of linear thermal expansion of iron is $10 \times 10^{-6} {^{\circ}C^{-1}}$,the increase in the length of the bar is .......... $cm$.

$A$ silver rod of $100 \; cm$ at $0^{\circ} C$ is heated to $100^{\circ} C$. Its length increases by $0.19 \; cm$. The coefficient of cubical expansion of the silver rod is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module