(D) The change in length (diameter) required is $\Delta L = L_2 - L_1 = 6.241 \,cm - 6.230 \,cm = 0.011 \,cm$.The formula for linear thermal expansion

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(D) The change in length (diameter) required is $\Delta L = L_2 - L_1 = 6.241 \,cm - 6.230 \,cm = 0.011 \,cm$.The formula for linear thermal expansion is $\Delta L = L_1 \alpha_L \Delta T$,where $\Delta T = T_f - T_i$.Substituting the given values: $0.011 = 6.230 \times (1.4 \times 10^{-5}) \times (T_f - 27)$.Solving for $\Delta T$: $\Delta T = \frac{0.011}{6.230 \times 1.4 \times 10^{-5}} = \frac{0.011 \times 10^5}{8.722} \approx 126.11^{\circ} C$.Therefore,the final temperature $T_f = 27 + 126.11 = 153.11^{\circ} C$.Comparing with the given options,the closest value is $152.7^{\circ} C$.

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Thermal Expansion for Solid

Medium

At what temperature (in $ ^{\circ} C$) should a gold ring of diameter $6.230 \,cm$ be heated so that it can be fitted on a wooden bangle of diameter $6.241 \,cm$ (in $.7$)? Both diameters were measured at room temperature $(27^{\circ} C)$. (Given: coefficient of linear thermal expansion of gold $\alpha_{L}=1.4 \times 10^{-5} \,K ^{-1}$)

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A
$125$
B
$91$
C
$425$
D
$152$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Thermal Expansion for Solid

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The temperature of a wire of length $1 \, m$ and area of cross-section $1 \, cm^2$ is increased from $0^\circ C$ to $100^\circ C$. If the rod is not allowed to increase in length,the force required will be $(\alpha = 10^{-5} /^\circ C$ and $Y = 10^{11} \, N/m^2)$.

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The ratio of linear expansion coefficient,area expansion coefficient,and volume expansion coefficient is ...............

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$A$ clock pendulum made of invar has a period of $0.5 \, s$ at $20^{\circ} C$. If the clock is used in a climate where the temperature averages to $30^{\circ} C$, how much time does the clock lose in each oscillation? (For invar, $\alpha = 9 \times 10^{-7} /{ }^{\circ} C$, $g = \text{constant}$)

The temperature of a wire of length $1 \, m$ and area of cross-section $1 \, cm^2$ is increased from $0^\circ C$ to $100^\circ C$. If the rod is not allowed to increase in length,the force required will be $(\alpha = 10^{-5} /^\circ C$ and $Y = 10^{11} \, N/m^2)$.

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