The coefficients of linear expansions of brass and steel are α₁ and α₂ respectively. When we take a brass rod of length l₁ and a steel rod of length l₂ at 0, then the difference in their lengths (l₂ - l₁) will remain the same at all temperatures if (a) α₁ l₁ = α₂ l₂ (b) α₁ l₂ = α₂ l₁ (c) α₁² l₂ = α₂² l₁ (d) α₁ l₂² = α₂ l₁²

Answer: (a). At temperature θ: l₂' - l₁' = (l₂ - l₁) + (l₂α₂ - l₁α₁)θ. The difference stays constant only if the two expansions are equal: l₁α₁ = l₂α₂. So the answer is (a) α₁ l₁ = α₂ l₂.

The coefficients of linear expansions of brass and steel are α₁ and… | NEET 1999 (AIPMT)

Q72NEET 1999 · AIPMTMedium

Thermometry & Thermal Expansion

The coefficients of linear expansions of brass and steel are $\alpha_1$ and $\alpha_2$ respectively. When we take a brass rod of length $l_1$ and a steel rod of length $l_2$ at $0^\circ\text{C}$ , then the difference in their lengths $(l_2 - l_1)$ will remain the same at all temperatures if

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Answer: (a)

At temperature $\theta$ : $l_2' - l_1' = (l_2 - l_1) + (l_2\alpha_2 - l_1\alpha_1)\theta$ .
The difference stays constant only if the two expansions are equal: $l_1\alpha_1 = l_2\alpha_2$ .
So the answer is (a) $\alpha_1 l_1 = \alpha_2 l_2$ .

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