Adiabatic Expansion of a Perfect Monoatomic Gas

Adiabatic expansion refers to a process in which a gas expands without gaining or losing heat to its surroundings. In this case, we are considering a perfect monoatomic gas, which means that the gas consists of individual atoms and does not have any internal rotational or vibrational degrees of freedom.

Percentage Increase in Volume

Given that the volume of the gas increases by 24%, we can calculate the final volume (Vf) using the initial volume (Vi) and the percentage increase:

Vf = Vi + (24/100) * Vi
= Vi * (1 + 0.24)
= 1.24 * Vi

Percentage Decrease in Pressure

To calculate the percentage decrease in pressure (P), we need to use the relationship between pressure and volume for an adiabatic process. According to the adiabatic equation, the product of pressure and volume raised to the power of the ratio of specific heat capacities (γ) is constant:

P * V^γ = constant

Since we are considering a perfect monoatomic gas, the value of γ is equal to 5/3. We can use this equation to express the final pressure (Pf) in terms of the initial pressure (Pi) and volumes (Vi and Vf):

Pi * Vi^γ = Pf * Vf^γ

Substituting the value of Vf from the previous calculation:

Pi * Vi^γ = Pf * (1.24 * Vi)^γ

Simplifying the equation:

Pi = Pf * (1.24)^γ

The percentage decrease in pressure can be calculated as:

Percentage decrease in pressure = (Pi - Pf) / Pi * 100

Substituting the values and simplifying:

Percentage decrease in pressure = (Pi - Pf) / Pi * 100
= (Pi - Pf) / Pi * 100
= (Pi - (Pi * (1.24)^γ)) / Pi * 100
= (1 - (1.24)^γ) * 100

Since γ = 5/3:

Percentage decrease in pressure = (1 - (1.24)^(5/3)) * 100
≈ 29.98

Therefore, the percentage decrease in pressure is approximately 30%, which corresponds to option B.