What is the percentage increase in the volume of a gas when its pressure is decreased by 20% at constant temperature?

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Answer

If by keeping the temperature constant, the pressure of a gas is decreased by 20 %, then the percentage change in volume of the gas will be

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Text Solution

increases by 20%decreases by 20%increases by 25%decreases by 25%

Answer : C

Solution : According to Boyle.s law <br> `P_(1)V_(1)=P_(2)V_(2)` <br> As the pressure is decreased by 20%, so <br> `P_(2)=(80)/(100)P_(1)` <br> `P_(1)V_(1)=(80)/(100) P_(1)V_(2)` <br> `V_(1)=(80)/(100) V_(2)` <br> Percentage increase in volume`=(V_(2)-V_(1))/(V_(1)) xx 100 =(100-80)/(80)=25%`

Text Solution

increases by 20%decreases by 20%increases by 25%decreases by 25%

Answer : C

Solution :  According to Boyle's law, `p_(1)V_(1)=p_(2)V_(2)` <br> As, the pressure is decreases by 20% , therefore <br> `p_(2)=(80)/(100)p_(1) rArr p_(1)V_(1)= (80)/(100)p_(1)V_(2) rArrV_(1)=(80)/(100)V_(2)` <br> `therefore` Percentage increase in volume <br> `=(V_(2)-V_(1))/(V_(1))xx100=(100-82)/(80)xx100=25%`

Text Solution

increased by 20%decrease by 20%increased by 25%decreased by 25%

Answer : C

Solution : `P' = P - 20/100 P = 4/5 P` <br> As temperature is constant , PV = constant <br> `:. PV = 4/5 P xx V' or V' = 5/4 V` <br> `:. % "increase in volume" =((V'-V)/(V)) xx 100` <br> `=((5/4V_(1)-V)/(V)) xx 100 = 25%`.