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Question

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

A
+ 20 %
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B
- 20 %
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C
+ 25 %
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D
- 25 %
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Solution

The correct option is C + 25 %
According to Boyle's law, we know that
PV=constant at constant temperature
we can write that,
P1V1=P2V2 ..............(1)
Given,
P is decreased by 20 %
Thus,
Initial pressure (P1)=P
Final pressure (P2)=P20100P
Initial volume (V1)=V
Final volume (V2)=V
From (1), we can write that
PV=80100PV
V=80100V .......(2)
Percentage change in volume is given by,
Final volume (V) Initial volume (V)Initial volume (V)×100
Using (2) in the above formula, we get
VVV×100=1008080×100=+25 %
Thus, option (c) is the correct answer.

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