The temperature of an isotropic cubical solid of length `l_(0)`, density `rho_(0)` and coefficient of linear expansion `alpha` is increased by `20^(@)C`. Then at higher temperature , to a good approximation:-

Options

A. (a)Length is `l_(0) (1+20alpha)`
B. (b)Total surface area is `l_(0)^(2) (1 +40alpha)`
C. (c)Total volume is `l_(0)^(3)(1+60alpha)`
D. (d)Density is `(rho_(0))/(1+ 60 alpha)`

Answer

A, C, D

Explanation

Length
`l = l_(0) (1+alphaDeltaT) = l_(0) (1+20alpha)`
Area
` A =A_(0) (1+betaDeltaT) = 6l_(0)^(2)(1+40alpha)`
Volume
` V=V_(0) (1+gammaDeltaT) = l_(0)^(3) ( 1+3alphaDeltaT) = l_(0)^(3) (1+60alpha)`
Density
`rho = (rho_(0))/(1+gammaDeltaT) = (rho_(0))/(1+60alpha)`