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A Carnot engine whose efficiency i...

A Carnot engine whose efficiency is 45% takes heat from a source maintained at a temperature of `327^(@)C` .To have an engine of efficiency 60% what must be the intake temperature for the same exhaust (sink) temperature

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Efficiency of Carnot engine `eta_(1) = 45%`
Efficiency of Carnot temperature of source `T_(1) = 327^(@) C`
Efficiency of Carnot temperature of sink `T_(2) = ?`
`= 327 + 273 = 600 k`
Efficiency of carnot temperature `eta _(2) = 60 %`
when efficiency of Carnot temperature of source `T=? `
`eta _(1) = 1- (T_(2))/(T_(1))`
`0.45 = 1- (T_(2))/(600)`
`0.45 xx 600 = 600 - T_(2)`
`T_(2) = 600 - 270 = 330`
`eta _(2) = 1- (T_(1))/(T_(2))`
`0.60 = 1- (330)/(T_(2))`
`0.60 T_(2) = T_(2) - 330`
`0.60 T_(2) + 330 = T_(2)`
`330 = T_(2) (1 - 0.60)`
`330 = 0. 40 T_(2)`
` :. , T_(2) = (330)/(0.40) = 825 k`
`= 825 - 273`
`T_(2) = 552^(@) C`
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