Driver of a truck gets his steel petrol tank filled with `75 L` of petrol at `10^(@)C`. If a `alpha_("steel")` is `12 xx 10^(-6)//.^(@)C` and `gamma_("pet")` is `9.5 xx 10^(-4)//.^(@)C` the overflow of petrol at `30^(2)C` is -

Options

A. 1.35L
B. 1.38 L
C. 1.45L
D. 1.48L

Answer

B

Explanation

Change in volume of petrol,
`Delta V_(P) = V_(gamma_(p)) Delta T = V xx 9.9 xx 10^(-4) xx 20 = 1.98 xx 10^(-2)V`
Change in volume of steel tank, `Delta V_(s) = V_(gamma_(s)) Delta T = V xx 3 xx 24 xx 10^(-6) xx 20`
`=1.44 xx 10^(-3) V= 0.144 xx 10^(-2)V`
Volume of petrol overflowing.
`DeltaV_(p) - Delta V_(s) = (1.98 - 0.144) xx 10^(-2)V`
`=1.836 xx 10^(-2) xx 75 = 1.38L`