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