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 $V_2=0.95V_1$ .
- Substitute all the known values in the above formula to get the amount of pressure increased.
$$\begin{array}{rl}& P_1{V}_1=P_2{V}_2\\ & P_2={\displaystyle \frac{P_1}{0.95}}\\ & P_2=1.0526P_1\end{array}$$

- Increase in pressure can be calculated as follows.
$$\begin{array}{rl}& =P_2-P_1\\ & =1.0526P_1-P_1\\ & =0.0526P_1\\ & =5.26\text{ \% }\end{array}$$
- 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.