The ratio of specific heat capacities at constant pressure to that at constant volume for a given mass of a gas is 5 2 . If the percentage increase in volume of the gas while undergoing an adiabatic change is 3 2 , then the percentage decrease in pressure will be:

Step-by-step solution

The ratio of specific heat capacities is given as = C_p C_v = 5 2 . For an adiabatic process, the relation between pressure and volume is PV^ = constant . Taking the logarithmic derivative, we get dP P + dV V = 0 , which implies dP P = - dV V . The percentage increase in volume is dV V 100 = 3 2 = 1.5 . Substituting the values, the percentage change in pressure is dP P 100 = - ( dV V 100 ) = - 5 2 3 2 = - 15 4 . The negative sign indicates a decrease in pressure. Thus, the percentage decrease in pressure is 15 4 .