Question

Length of 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 `(alpha)` of the given wire is
A. `5.021 xx 10^(-5) K^(-1)`
B. `6.021 xx 10^(-5) K^(-1)`
C. `7.021 xx 10^(-5) K^(-1)`
D. `8.021 xx 10^(-5) K^(-1)`

Answer 1

Correct Answer - D
Here, `T_(1) = 27^(@)C = 273+ 27 = 300 K`
`T_(2) = 100^(@)C = 273 + 100 = 373 K`
`L_(1) = 4.55 m , L_(2) = 4.57 m`
As, `L_(2) = L_(1)[1+alpha(T_(2) - T_(1))]`
`:. 4.57 = 4.55 [1+alpha(373-300)]`
`4.57 = 4.55 [1+alphaxx273]`
or `alpha = [(4.57)/(4.55)-1] xx 1/73 = [(4.57 - 4.55)/(4.55)] xx 1/73`
`alpha = 6.021 xx 10^(-5) K^(-1)`