Question

Choose the correct option.

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

Options

• Decrease by 9%

• Increase by 9%

• Decrease by 10%

• Increase by 11.11%

Answer 1

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 = 9/10`

Substitute `9/10` for `P_2/P_1` to find the % change in volume.

`V_2/V_1 = 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 = `[10/9 - 1] xx 100%`

%V = `[1/9] xx 100%`

Simplify the above equation.

%V = 0.1111 × 100%

%V = 11.11%