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In a petrol engine (internal combusti...

In a petrol engine (internal combustion engine ) air at atmospheric pressure and temperature of `20^(@)C` is compressed in the cylinder by the piston to `1//8` of its original volume . Calculate the termperature of the compressed air .

Text Solution

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At temperature `T_(1)`
Atmospheric pressure of air = 1 atm
Initial volume of air `V_(1) = V m^(3)`
Initial temperature of air `T_(1) = 20^(@)C`
`=20 + 273 = 293 K`
At temperature `T_(2)`
volume of the air is compressed by a factor of `(1)/(8)`
The new Volume `V_(2) = V.(1)/(8) m^(3)`
`gamma =1.4`
The atmospheric pressure of the gas at final temperature `T_(2) = ? `
Equation of ideal gas `(P_(1)V_(1))/(T_(1))= (P_(2)V_(2))/(T_(2))`
`T_(2) = T_(1) .((V_(1))/(V_(2))) ^(gamma -1)`
`T_(2) = 293 .((V)/((V)/(8)))^(gamma-1)`
`T_(2) = 293 (8 )^(gamma-1) =293 xx (8)^(1.4-1)`
`= 293 xx (8)^(0.4) = 673. 1^(@)C`
`T_(2) = 673 - 273 `
`T_(2) = 400^(@)C`
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