Question 748: Thermodynamics & KTG

Question

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

Accepted Answer

To find the increase in length of a metal rod due to temperature change, you can use the formula:
$ \mathrm{d}l = \alpha 	imes l 	imes \mathrm{dt} $
where:
$\alpha$ is the coefficient of linear expansion.
$l$ is the original length of the rod.
$\mathrm{dt}$ is the change in temperature.
For this problem:
$\alpha = 2 	imes 10^{-5} /^{\circ} \mathrm{C}$
$l = 0.75 \, 	ext{m}$
The temperature change, $\mathrm{dt} = 65^{\circ}\mathrm{C} - 45^{\circ}\mathrm{C} = 20^{\circ}\mathrm{C}$
Substitute these values into the formula:
$ \mathrm{d}l = 2 	imes 10^{-5} 	imes 0.75 	imes 20 $
$ \mathrm{d}l = 0.3 	imes 10^{-3} \mathrm{m} = 0.30 \, \mathrm{mm} $
Thus, the increase in length of the rod is 0.30 mm.

Answer

3.0 mm

Answer

0.75 mm

Answer

0.30 mm

Answer

0.15 mm

Thermodynamics & KTG

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

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