Answer:
75%
Explanation:
We'll begin by calculating the final volume of the gas. This can be obtained as follow:
Initial volume (V₁) = V
Initial temperature (T₁) = T
Initial pressure (P₁) = P
Final pressure (P₂) = 2P
Final temperature (T₂) = ½T
Final volume (V₂) =?
P₁V₁/T₁ = P₂V₂/T₂
PV/T = 2P × V₂ / ½T
Cross multiply
T × 2P × V₂ = PV × ½T
T × 2P × V₂ = PV × ½T
Divide both side by T × 2P
V₂ = (PV × ½T) / T × 2P
V₂ = ¼V
Next, we shall determine the absolute change in the volume of the gas. This can be obtained as follow:
Initial volume (V₁) = V
Final volume (V₂) = ¼V
Absolute change in volume |ΔV| =?
|ΔV| = |V₂ – V₁|
|ΔV| = |¼V – V|
|ΔV| = |0.25V – V|
|ΔV| = 0.75V
Finally, we shall determine percentage change in the volume of the gas. This can be obtained as follow:
Initial volume (V₁) = V
Absolute change in volume |ΔV| = 0.75V
Percentage change =?
Percentage change = |ΔV| / V × 100
Percentage change = 0.75V / V × 100
Percentage change = 0.75 × 100
Percentage change = 75%
Thus, the percentage change in the volume of the gas is 75%
