Question 653: Thermodynamics & KTG

Question

The volume of a metal sphere increases by $0.33 \%$ when its temperature is raised by $50^{\circ} \mathrm{C}$. The coefficient of linear expansion of the metal is

Accepted Answer

Step 1: Recall relation between volumetric and linear expansion.
Volumetric expansion coefficient: $\beta = 3\alpha$
where $\alpha$ = coefficient of linear expansion.
Relative change in volume:
$ \frac{\Delta V}{V} = \beta \Delta T = 3\alpha \Delta T $
Step 2: Express given data.
Percentage change in volume = $0.33\% = 0.0033$ (in decimal).
So,
$ \frac{\Delta V}{V} = 0.0033 $
Temperature rise = $\Delta T = 50^\circ \mathrm{C}$.
Step 3: Use formula.
$ 0.0033 = 3\alpha (50) $
$ 0.0033 = 150\alpha $
$ \alpha = \frac{0.0033}{150} $
$ \alpha = 2.2 	imes 10^{-5} / ^\circ \mathrm{C} $
Ã¢ÂÂ Final Answer:
$ \boxed{2.2 	imes 10^{-5} / ^\circ \mathrm{C}} $
Correct option: A

Answer

$2.2 	imes 10^{-5} /{ }^{\circ} \mathrm{C}$

Answer

$6.6 	imes 10^{-5} /{ }^{\circ} \mathrm{C}$

Answer

$13.2 	imes 10^{-5} /{ }^{\circ} \mathrm{C}$

Answer

$19.8 	imes 10^{-5} /{ }^{\circ} \mathrm{C}$

Thermodynamics & KTG

The volume of a metal sphere increases by 0.33 \% when its temperature is raised by 50^{\circ} \mathrm{C}. The coefficient of linear expansion of the metal is

Choose the correct answer: