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Standard IX

Physics

Thermal Expansion

A thin copper...

Question

A thin copper wire of length $l$ increases its length by 1% when heated from temperature $T_{1}$ to $T_{2}$ . What is the percentage change in area when a thin copper plate having dimensions $2 l \times l$ is heated from $T_{1}$ to $T_{2}$ ?

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Solution

The correct option is B
2%

We know that, $Δ l = α l Δ T$
$\Rightarrow \frac{1}{100} l = α l (T_{2} - T_{1})$
$\Rightarrow α (T_{2} - T_{1}) = 0.01$
Now, coefficient of area expansion, $β = 2 α$
So, increase in area, $Δ A = β A Δ T = 2 α A (T_{2} - T_{1})$
$\Rightarrow \frac{Δ A}{A} = 2 α (T_{2} - T_{1}) = 0.02$
Hence, percentage increase in area is 2% and the correct option is (b).

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Similar questions

A thin copper wire of length $l$ increases its length by 1% when heated from temperature $T_{1}$ to $T_{2}$ . What is the percentage change in area when a thin copper plate having dimensions $2 l \times l$ is heated from $T_{1}$ to $T_{2}$ ?

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A thin copper wire of length l increases its length by 1% when heated from temperature T1 to T2. What is the percentage change in area when a thin copper plate having dimensions 2l×l is heated from T1 to T2?

The correct option is B 2% We know that, Δl=αlΔT ⇒1100l=αl(T2−T1) ⇒α(T2−T1)=0.01 Now, coefficient of area expansion, β=2α So, increase in area, ΔA=βAΔT=2αA(T2−T1) ⇒ΔAA=2α(T2−T1)=0.02 Hence, percentage increase in area is 2% and the correct option is (b).

A thin copper wire of length $l$ increases its length by 1% when heated from temperature $T_{1}$ to $T_{2}$ . What is the percentage change in area when a thin copper plate having dimensions $2 l \times l$ is heated from $T_{1}$ to $T_{2}$ ?