If a petrol tank costs σ2000.00 to fill it up at 10°C,how much extra must I pay to fill up the tank at 50°C if the petrol costs σ50.00 per litre and its cubic expansivity is 9.5×10^(−4) K^(−1) ?


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Question Number 42125 by Necxx last updated on 18/Aug/18

$I f a p e t r o l t a n k c o s t s σ 2000.00 t o$ $f i l l i t u p a t 10 ° C, h o w m u c h e x t r a$ $m u s t I p a y t o f i l l u p t h e t a n k a t 50 ° C$ $i f t h e p e t r o l c o s t s σ 50.00 p e r l i t r e$ $a n d i t s c u b i c e x p a n s i v i t y i s$ $9.5 \times 10^{- 4} K^{- 1} ?$
Commented by Necxx last updated on 18/Aug/18

$I t r i e d i t t h u s b u t w a s n t c o n v i n c e d$ $s i n c e γ = \frac{Δ V}{V Δ θ} t h e n$ $\frac{Δ V}{V} = γ Δ θ = 9.5 \times 10^{- 4} \times (50 - 10)$ $= 9.5 \times 40 \times 10^{- 4}$ $= 3.8 \times 10^{- 2}$ $∴ t h e e x t r a a m o u n t = 50 \times 3.8 \times 10^{- 2}$ $= σ 1.9$ $p l e a s e c h e c k a n d c o r r e c t m e$
Commented by Necxx last updated on 18/Aug/18

$p l e a s e h e l p i t s u r g e n t$
Commented by MrW3 last updated on 18/Aug/18

$t h e e x t r a a m o u n t = 2000 \times 3.8 \times 10^{- 2}$
Commented by Necxx last updated on 18/Aug/18

$T h a n k s . . . T h o u g h I t h o u g h t i t w a s$ $σ 50.00 p e r v o l u m e s o I f e l t t h e$ $i n c r e a s e s h o u l d b e i n r e l a t i o n t o$ $t h a t .$
Commented by MrW3 last updated on 18/Aug/18

$V c o s t s C$ $Δ V c o s t s Δ C$ $\frac{Δ C}{C} = \frac{Δ V}{V}$ $\Rightarrow Δ C = C \times \frac{Δ V}{V} = 2000 \times \frac{Δ V}{V} = . . . . . .$ $σ 50 i s t h e c o s t f o r o n e l i t r e, n o t t h e$ $c o s t f o r a t a n k .$
Commented by Necxx last updated on 18/Aug/18

${I t}^{'} s c l e a r n o w . . . T h a n k y o u s o m u c h$
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