Length of a wire at room temperature is 4.55 m, when the temperature increases upto 100°C then its length becomes 4.57 m. The coefficient of linear expansion (α) of the given wire is

Question

Length of a wire at room temperature is 4.55 m, when the temperature increases upto 100°C then its length becomes 4.57 m. The coefficient of linear expansion (α) of the given wire is (A) 5.021 × 10-5 K-1 (B) 6.021 × 10-5 K-1 (C) 7.021 × 10-5 K-1 (D) 8.021 × 10-5 K-1

Tardigrade Admin · Accepted Answer

Here, T1=27°C=273+27=300 K T2=100°C=273+100=373 K L1=4.55 m, L2=4.57 m As, L2=L1 [1+α(T2-T1)] ∴ 4.57=4.55[1+α(373-300)] 4.57=4.55[1+α × 73] or α=[(4.57/4.55)-1]×(1/73)=[(4.57-4.55/4.55)]×(1/73) α=6.021 ×10-5 K-1

Q. Length of a wire at room temperature is $4.55 m$ , when the temperature increases upto $10 0^{\circ} C$ then its length becomes $4.57 m$ . The coefficient of linear expansion $(α)$ of the given wire is

$5.021 \times 1 0^{- 5} K^{- 1}$

$6.021 \times 1 0^{- 5} K^{- 1}$

$7.021 \times 1 0^{- 5} K^{- 1}$

$8.021 \times 1 0^{- 5} K^{- 1}$

Q. Length of a wire at room temperature is 4.55m, when the temperature increases upto 100∘C then its length becomes 4.57m. The coefficient of linear expansion (α) of the given wire is

5.021×10−5K−1

6.021×10−5K−1

7.021×10−5K−1

8.021×10−5K−1

Here, T1​=27∘C=273+27=300K T2​=100∘C=273+100=373K L1​=4.55m, L2​=4.57m As, L2​=L1​[1+α(T2​−T1​)] ∴4.57=4.55[1+α(373−300)] 4.57=4.55[1+α×73] or α=[4.554.57​−1]×731​=[4.554.57−4.55​]×731​ α=6.021×10−5K−1

Q. Length of a wire at room temperature is $4.55 m$ , when the temperature increases upto $10 0^{\circ} C$ then its length becomes $4.57 m$ . The coefficient of linear expansion $(α)$ of the given wire is

$5.021 \times 1 0^{- 5} K^{- 1}$

$6.021 \times 1 0^{- 5} K^{- 1}$

$7.021 \times 1 0^{- 5} K^{- 1}$

$8.021 \times 1 0^{- 5} K^{- 1}$