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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

A
Both A and B are correct
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B
A is correct but B is wrong
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C
B is a correct but A is wrong
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D
Both A and B are wrong
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Solution

## The correct option is D Both A and B are correctThe coefficient of linear expansion is given by: α=Δll×Δt where, l=1m(let)= initial length of rod Δl=1m(let)= change in length of rod Δt=1K(let)= change in temperature Now, α=1m1m×1K=1K−1 Similarly, the coefficient of volume expansion is given by: γ=ΔVV×Δt where, V=1m3(let)= initial volume ΔV=1m3(let)= change in volume Δt=1K(let)= change in temperature Now, γ=1m31m3×1K=1K−1 Hence both α and γ have the dimension K−1.

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