The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula α = aT , where a is a constant and T in °C. If the length of the rod is ℓ at temperature 0 ∘ C , the

Question

The co-efficient of thermal expansion of a rod is temperature dependent and is given by the formula $α = aT$ , where a is a constant and T in °C. If the length of the rod is $ℓ$ at temperature $0^{\circ} C$ , then the temperature at which the length will be $2 ℓ$ is :

Options:

Answer:

B

Solution:

$\frac{d L}{L} = a T d T$
Integrating gives
$ln 2 = \frac{a T ^{2}}{2}$
$T = \frac{ln 4}{a}$

TestHub · Accepted Answer

L d L ​ = a T d T Integrating gives ln 2 = 2 a T 2 ​ T = a ln 4 ​ ​

Physics - Heat & Thermo Question with Solution | TestHub

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