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At 3 atm and 17^(@)C a gas cylinder has ...

At 3 atm and `17^(@)C` a gas cylinder has a volume of 10 litre. If the temperature of cylinder is increased to `47^(@)C`, how many litres of air measured at `47^(@)C` and pressure of 1 atm should be let out to restore the pressure to 3 atm at `47^(@)C` ?

Text Solution

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`(P_(1))/(T_(1))=(P_(2))/(T_(2)) implies (3)/(290)= (P_(2))/(320)implies P_(2)=3.31atm` Pressure to be decreased in cylinder = 3.31 – 3.00 = 0.31 atm.  Let the volume of the gas to be taken out at 1 atm be V. As the temperature remains constant Boyle’s law can be applied to determine V as follows
`P_(1)V_(1)=P_(2)V_(2) implies 1 xx V= 0.31xx10implies V= 3.1 liter"`
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