Question

How much the pressure should be increased at a constant temperature to reduce the volume of an ideal gas by $20$%?

• A. $16.67$%
• B. $20$%
• C. $22.22$%
• D. $25$%

Answer 1

The correct option is D $25$%

Given :

volume of an ideal gas is reduced by 20% keeping temperature constant

solution :

by using ideal gas equation ,

$PV=nRT$

aas nRT is constant so whole PV is constant

$PaVa=PbVb$

$\Rightarrow$ $PaVa=Pb[Va-\frac{20}{100}Va]$

$\Rightarrow$ $Pa=Pb\left[\frac{4}{5}\right]$

$\Rightarrow$ percentage change in pressure is equals to

$\frac{Pb-Pa}{Pa}$ X 100

$\Rightarrow$ $\frac{Pb-\frac{4}{5}Pb}{\frac{4}{5}Pb}$x 100

$\Rightarrow$ 25%

hence the correct option is:D