Question

If the pressure of an ideal gas decreases by $10\%$ isothermally, then its volume will ___________.

• A. Increase by $11\%$
• B. Increase by $7\%$
• C. Increase by $10\%$
• D. Increase by $14\%$

Answer 1

The correct option is A Increase by $11\%$

Ideal gas equation is given by, $PV=RT$

For a isothermal process, the temperature remains constant. So if pressure decreases so the volume will increase.

Thus, $P_1{V}_1=P_2{V}_2$ or $P_1/P_2=V_2/V_1$

Here, $P_2=P_1-P_1/10=\left(9P_1/10\right)$ or $P_2/P_1=9/10$

So, $V_2/V_1=10/9$

The % of volume increase $=\left[\right(V_2-V1\left)/V_1\right]\times 100=\left[\right(V_2/V_1)-1]100=\left[\right(10/9)-1]100=11.1$ %