To solve this problem, we can use the relation for an adiabatic process, which is given as:
PVγ=‌ constant ‌Where
P is the pressure,
V is the volume, and
γ (gamma) is the heat capacity ratio. In an adiabatic process, as the volume increases, the pressure decreases. We are given that the volume increases by
6.2%, so we can express the final volume
Vf in terms of the initial volume
Vi as:
Vf=Vi+0.062Vi=1.062ViUsing the relation for an adiabatic process for both initial and final states, we have:
PiViγ=PfVfγSubstituting the expression for
Vf, we get:
PiViγ=Pf(1.062Vi)γ ‌‌=(‌)γ‌‌=(1.062)−γGiven that
γ=1.4, let's substitute that into the equation:
‌=(1.062)−1.4We can now calculate the percentage change in pressure. However, remember that the percentage change is given by:
Percentage Change
=(‌)×100%But since we are finding
‌ directly, we need to adjust our formula to:
Percentage Change
=(‌−1)×100%Substituting our value for
‌ :
Percentage Change
=((1.062)−1.4−1)×100%Computing the value
(1.062)−1.4.
=((1.062)−1.4−1)×100%≈(−0.0868)×100%=−8.68%Since a negative sign indicates a decrease in pressure, the answer implies that the pressure decreases by approximately
8.68%. Thus, the correct answer is Option
A:8.68.