In an adiabatic expansion of air, the volume is increased by 6.2 % . The percentage change in pressure is ( =1.4)

Step-by-step solution

For an adiabatic process, the relation between pressure P and volume V is given by PV^ = constant . Taking the logarithmic differentiation of the equation PV^ = C , we get P + V = C . Differentiating both sides, we obtain dP P + dV V = 0 , which implies dP P = - dV V . Given that the volume increases by 6.2 % , we have dV V = 0.062 . Substituting the values = 1.4 and dV V = 0.062 into the expression for the fractional change in pressure: dP P = -1.4 0.062 = -0.0868 . The percentage change in pressure is dP P 100 =