Choose the correct option. If the pressure of an ideal gas decreases by 10% isothermally, then its volume will ______.

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If the pressure of an ideal gas decreases by 10% isothermally, then its volume will increase by 11.11% Explanation: Express the relation of the Ideal gas equation. PV = RT ......(i) Here, P is pressure, V is volume, R is the universal gas constant and R is temperature. Since the process is isothermal, therefore, the temperature remains constant. Substitute P1 for P and V1 for V to obtain the initial ideal gas equation. P1V1 = RT ......(ii) Here P1 is the initial pressure and V1 is the initial volume. Substitute P2 for P and V2 for V to obtain the final ideal gas equation. P2V2 = RT ......(iii) Here, P2 is final pressure and V2 is the final volume. Equating equation (ii) and equation (iii). P1V1 = P2V2 P_1/V_2 = P_2/V_1 Express the relation between P2 and V2. P_2 oo 1/V_2 ......(iv) Express the relation between P1 and P2. P2 = P_1 − P_1/10 P2 = (9P_1)/10 P_2/P_1 = $\frac{9}{10}$ Substitute $\frac{9}{10}$ for P_2/P_1 to find the % change in volume. V_2/V_1 = $\frac{10}{9}$ Calculate the % change in volume. %V = [(V_2 - V_1)/(V_1)] xx 100% %V = [V_2/V_1 - 1] xx 100% %V = [$\frac{10}{9}$ - 1] xx 100% %V = [$\frac{1}{9}$] xx 100% Simplify the above equation. %V = 0.1111 $\times$ 100% %V = 11.11%

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