Question

At a constant temperature what should be the percentage increase in pressure for a 5 % decreases in the volume of gas:
A. 5 %
B. 10 %
C. 5.26 %
D. 4.26 %

Answer 1

Hint: We can find the relationship between volume and pressure in the ideal gas equation and it is as follows.
PV = nRT
P = Pressure of the gas
V = Volume of the gas
n = number moles of the gas
R = Gas constant
T = Temperature of the gas

Complete Solution :
- In the question it is given that there is a decrease of volume of the gas by 5 % at constant temperature.
- We are supposed to find the percentage of the increase of pressure for a 5 % decrease in the volume of gas at constant temperature.
- At constant temperature we can use Boyle's law.
- The Boyle’s law can be expressed as
\[{{P}_{1}}{{V}_{1}} = {{P}_{2}}{{V}_{2}}\]

- In the question it is given that volume is decreased by 5 %. Then ${{V}_{2}} = 0.95{{V}_{1}}$ .
- Substitute all the known values in the above formula to get the amount of pressure increased.
\[\begin{align}
 & {{P}_{1}}{{V}_{1}} = {{P}_{2}}{{V}_{2}} \\
 & {{P}_{2}} = \dfrac{{{P}_{1}}}{0.95} \\
 & {{P}_{2}} = 1.0526{{P}_{1}} \\
\end{align}\]

- Increase in pressure can be calculated as follows.
\[\begin{align}
 & = {{P}_{2}}-{{P}_{1}} \\
 & = 1.0526{{P}_{1}}-{{P}_{1}} \\
 & = 0.0526{{P}_{1}} \\
 & = 5.26\text{ % }\!\!\!\!\text{ } \\
\end{align}\]
- The pressure is increased by 5.26 % when the volume of a gas is reduced by 5 % at a constant temperature.
So, the correct answer is “Option C”.

Note: We have to consider Boyle's law while calculating the increase in pressure when there is a decrease in volume at constant temperature. Then only we can get the increases in pressure of the gas accurately.