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Question
Consider the following statements.
(A) The coefficient of linear expansion has dimension K–1.
(B) The coefficient of volume expansion has dimension K–1.
Options
A and B are correct.
A is correct but B is wrong.
B is correct but A is wrong.
A and B are wrong.
Solution
(a) A and B are correct.
The coefficient of linear expansion,
`∝ =1/L (ΔL)/(ΔT)`
=`|L|/|LT| =K^-1`
Here, L = initial length
ΔL = change in length
ΔT = change in temperature
On the other hand, the coefficient of volume expansion,
γ = `1/V (ΔV)/(ΔT) = |L^3|/|L^3T| = K^-1`
Here, V = initial volume
Δ V = change in volume
ΔT = change in temperature
K = kelvin, the S.I. unit of temperature
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