SATHEE: Thermal Properties of Matter

Thermal Properties of Matter - Result Question 2

2. Coefficient of linear expansion of brass and steel rods are $α_{1}$ and $α_{2}$ . Lengths of brass and steel rods are $ℓ_{1}$ and $ℓ_{2}$ respectively. If $(ℓ_{2} - ℓ_{1})$ is maintained same at all temperatures, which one of the following relations holds good?

[2016, 1999, 1995]

(a) $α_{1} ℓ_{2_{2}} = α_{2} ℓ_{1_{2}}$

(b) $α_{1} ℓ_{2} = α_{2} ℓ_{1}$

(d) $α_{1} ℓ_{1} = α_{2} ℓ_{2}$

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Answer:

Correct Answer: 2. (d)

Solution:

(d) From question, $(ℓ_{2} - ℓ_{1})$ is maintained same at all temperatures hence change in length for both rods should be same

i.e., $Δ ℓ_{1} = Δ ℓ_{2}$

As we know, coefficient of linear expansion,

$α = \frac{Δ ℓ}{ℓ_{0} Δ T}$

$ℓ_{1} α_{1} Δ T = ℓ_{2} α_{2} Δ T$

$ℓ_{1} α_{1} = ℓ_{2} α_{2}$

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Thermal Properties of Matter - Result Question 2

2. Coefficient of linear expansion of brass and steel rods are α1 and α2. Lengths of brass and steel rods are ℓ1 and ℓ2 respectively. If (ℓ2−ℓ1) is maintained same at all temperatures, which one of the following relations holds good?

Answer:

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2. Coefficient of linear expansion of brass and steel rods are $α_{1}$ and $α_{2}$ . Lengths of brass and steel rods are $ℓ_{1}$ and $ℓ_{2}$ respectively. If $(ℓ_{2} - ℓ_{1})$ is maintained same at all temperatures, which one of the following relations holds good?