During an adiabatic process on a gas having = 1.4 , its pressure increases by 0.5 % . The volume of the gas decreases by approximately

Step-by-step solution

For an adiabatic process, the relation between pressure and volume is given by: P V^ = constant Taking the natural logarithm on both sides: P + V = constant Differentiating both sides for small changes, we get: P P + V V = 0 - V V = 1 P P Multiplying by 100 to express in terms of percentage: - V V 100 = 1 ( P P 100 ) Given that the pressure increases by 0.5 % ( P P 100 = 0.5 ) and = 1.4 , the percentage decrease in volume is: - V V 100 = 0.5 1.4 = 5 14 0.357 % Rounding off to two decimal places, the volume decrease