解：?$(1)$?合格的?$500\ \mathrm {mL}$?的?$50°$?白酒中酒精的體積?$V_{酒精}=500\ \mathrm {mL}×50\%=250\ \mathrm {mL}=250\ \mathrm {cm}^3，$?
酒精的質(zhì)量?$m_{酒精}=ρ_{酒精}\ \mathrm {V}_{酒精}=0.8\ \mathrm {g/cm}^3×250\ \mathrm {cm}^3=200\ \mathrm {g}，$?
白酒中水的體積?$V_{水}=V-V_{酒精}=500\ \mathrm {cm}^3-250\ \mathrm {cm}^3=250\ \mathrm {cm}^3，$?
水的質(zhì)量?$m_{水}=ρ_{水}\ \mathrm {V}_{水}=1\ \mathrm {g/cm}^3×250\ \mathrm {cm}^3=250\ \mathrm {g}，$?
白酒的平均密度為?$ρ=\frac {m_{酒精}+m_{水}}{V}=\frac {200\ \mathrm {g}+250\ \mathrm {g}}{500\ \mathrm {cm}^3}=0.9\ \mathrm {g/cm}^3=0.9×10^3\ \mathrm {kg/m}^3；$?
?$(2)$?設(shè)白酒中酒精的體積為?$V_{酒精}，$?則水的體積為?$V-V_{酒精}，$?
酒精的質(zhì)量為?$ρ_{酒精}\ \mathrm {V}_{酒精}，$?水的質(zhì)量為?$ρ_{水}(V-V_{酒精})，$?
白酒的質(zhì)量為?$ρ_{酒精}\ \mathrm {V}_{酒精}+ρ_{水}(V-V_{酒精})=m_{白酒}，$?
即：?$0.8\ \mathrm {g/cm}^3×V_{酒精}+1\ \mathrm {g/cm}^3×(500\ \mathrm {cm}^3-V_{酒精})=455\ \mathrm {g}，$?
解得：?$V_{酒精}=225\ \mathrm {cm}^3，$?
白酒的實(shí)際度數(shù)為?$\frac {V_{酒精}}{V}=\frac {225\ \mathrm {cm}^3}{500\ \mathrm {cm}^3}=45°＜50°$?
由此可知被抽查白酒的實(shí)際度數(shù)沒有達(dá)到其標(biāo)注的度數(shù)；
?$(3)$?設(shè)白酒的體積為?$V，$?則白酒中酒精的體積為?$\frac {TV}{100}，$?水的體積為?$V-\frac {TV}{100}，$?
白酒的質(zhì)量為?$ρ_{白酒}\ \mathrm {V}，$?白酒中酒精的質(zhì)量為?$ρ_{酒精}\frac {TV}{100}，$?水的質(zhì)量為?$ρ_{水}(V-\frac {TV}{100})，$?
由質(zhì)量關(guān)系得：?$ρ_{酒精}\frac {TV}{100}+ρ_{水}(V-\frac {TV}{100})=ρ_{白酒}\ \mathrm {V}，$?
整理得：?$T=\frac {100(ρ_{水}-ρ_{白酒})}{ρ_{水}-ρ_{酒精}}.$
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