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Question Number 42125 by Necxx last updated on 18/Aug/18
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) ?
$${If}\:{a}\:{petrol}\:{tank}\:{costs}\:\sigma\mathrm{2000}.\mathrm{00}\:{to} \\ $$$${fill}\:{it}\:{up}\:{at}\:\mathrm{10}°{C},{how}\:{much}\:{extra} \\ $$$${must}\:{I}\:{pay}\:{to}\:{fill}\:{up}\:{the}\:{tank}\:{at}\:\mathrm{50}°{C} \\ $$$${if}\:{the}\:{petrol}\:{costs}\:\sigma\mathrm{50}.\mathrm{00}\:{per}\:{litre} \\ $$$${and}\:{its}\:{cubic}\:{expansivity}\:{is} \\ $$$$\mathrm{9}.\mathrm{5}×\mathrm{10}^{−\mathrm{4}} {K}^{−\mathrm{1}} ? \\ $$
Commented by Necxx last updated on 18/Aug/18
I tried it thus but wasnt convinced  since  γ=((ΔV)/(VΔθ)) then  ((ΔV)/V)=γΔθ=9.5×10^(−4) ×(50−10)            =9.5×40×10^(−4)               =3.8×10^(−2)   ∴the extra amount=50×3.8×10^(−2)              =σ1.9  please check and correct me
$${I}\:{tried}\:{it}\:{thus}\:{but}\:{wasnt}\:{convinced} \\ $$$${since}\:\:\gamma=\frac{\Delta{V}}{{V}\Delta\theta}\:{then} \\ $$$$\frac{\Delta{V}}{{V}}=\gamma\Delta\theta=\mathrm{9}.\mathrm{5}×\mathrm{10}^{−\mathrm{4}} ×\left(\mathrm{50}−\mathrm{10}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:=\mathrm{9}.\mathrm{5}×\mathrm{40}×\mathrm{10}^{−\mathrm{4}} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:=\mathrm{3}.\mathrm{8}×\mathrm{10}^{−\mathrm{2}} \\ $$$$\therefore{the}\:{extra}\:{amount}=\mathrm{50}×\mathrm{3}.\mathrm{8}×\mathrm{10}^{−\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\sigma\mathrm{1}.\mathrm{9} \\ $$$${please}\:{check}\:{and}\:{correct}\:{me} \\ $$$$ \\ $$$$ \\ $$
Commented by Necxx last updated on 18/Aug/18
please help its urgent
$${please}\:{help}\:{its}\:{urgent} \\ $$
Commented by MrW3 last updated on 18/Aug/18
the extra amount=2000×3.8×10^(−2)
$${the}\:{extra}\:{amount}=\mathrm{2000}×\mathrm{3}.\mathrm{8}×\mathrm{10}^{−\mathrm{2}} \\ $$
Commented by Necxx last updated on 18/Aug/18
Thanks...Though I thought it was  σ50.00 per volume so I felt the  increase should be in relation to  that.
$${Thanks}…{Though}\:{I}\:{thought}\:{it}\:{was} \\ $$$$\sigma\mathrm{50}.\mathrm{00}\:{per}\:{volume}\:{so}\:{I}\:{felt}\:{the} \\ $$$${increase}\:{should}\:{be}\:{in}\:{relation}\:{to} \\ $$$${that}. \\ $$
Commented by MrW3 last updated on 18/Aug/18
V costs C  ΔV costs ΔC  ((ΔC)/C)=((ΔV)/V)  ⇒ΔC=C×((ΔV)/V)=2000×((ΔV)/V)=......  σ50 is the cost for one litre, not the  cost for a tank.
$${V}\:{costs}\:{C} \\ $$$$\Delta{V}\:{costs}\:\Delta{C} \\ $$$$\frac{\Delta{C}}{{C}}=\frac{\Delta{V}}{{V}} \\ $$$$\Rightarrow\Delta{C}={C}×\frac{\Delta{V}}{{V}}=\mathrm{2000}×\frac{\Delta{V}}{{V}}=…… \\ $$$$\sigma\mathrm{50}\:{is}\:{the}\:{cost}\:{for}\:{one}\:{litre},\:{not}\:{the} \\ $$$${cost}\:{for}\:{a}\:{tank}. \\ $$
Commented by Necxx last updated on 18/Aug/18
It′s clear now...Thank you so much
$${It}'{s}\:{clear}\:{now}…{Thank}\:{you}\:{so}\:{much} \\ $$$$ \\ $$

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