Question 742: Thermodynamics & KTG

Question

A sheet of steel is 40 cm long and 5 cm broad at $0^{\circ} \mathrm{C}$. The surface area of the sheet increases by $1.4 \mathrm{~cm}^2$ at $100^{\circ} \mathrm{C}$. Coefficient of linear expansion of steel is

Accepted Answer

To calculate the coefficient of linear expansion of steel, we start by considering the formula for the change in surface area due to thermal expansion:
$$ \Delta A = A_0 \cdot 2\alpha \cdot \Delta T $$
where:
$\Delta A$ is the change in area
$A_0$ is the original area
$\alpha$ is the coefficient of linear expansion
$\Delta T$ is the change in temperature
Given:
Original length $L_0 = 40 \, 	ext{cm}$
Original breadth $B_0 = 5 \, 	ext{cm}$
$\Delta A = 1.4 \, 	ext{cm}^2$
$\Delta T = 100^\circ 	ext{C} - 0^\circ 	ext{C} = 100^\circ 	ext{C}$
First, calculate the original area $A_0$:
$$ A_0 = L_0 	imes B_0 = 40 \, 	ext{cm} 	imes 5 \, 	ext{cm} = 200 \, 	ext{cm}^2 $$
Insert the known values into the formula to find $\alpha$:
$$ 1.4 \, 	ext{cm}^2 = 200 \, 	ext{cm}^2 \cdot 2\alpha \cdot 100^\circ 	ext{C} $$
Solve for $\alpha$:
$$ 1.4 = 200 	imes 200\alpha $$
$$ \alpha = \frac{1.4}{200 	imes 200} $$
$$ \alpha = \frac{1.4}{40000} $$
$$ \alpha = 0.000035 \, /^\circ 	ext{C} $$
Thus, the coefficient of linear expansion of steel is
$$ 3.5 	imes 10^{-5} /^\circ 	ext{C}. $$
So, the correct option is C: $3.5 	imes 10^{-5} /^\circ 	ext{C}$.

Answer

$1.9 	imes 10^{-5} /{ }^{\circ} \mathrm{C}$

Answer

$2.4 	imes 10^{-5} /^{\circ} \mathrm{C}$

Answer

$3.5 	imes 10^{-5} /^{\circ} \mathrm{C}$

Answer

$7 	imes 10^{-5} / \mathrm{C}$

Thermodynamics & KTG

A sheet of steel is 40 cm long and 5 cm broad at 0^{\circ} \mathrm{C}. The surface area of the sheet increases by 1.4 \mathrm{~cm}^2 at 100^{\circ} \mathrm{C}. Coefficient of linear expansion of steel is

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