An ideal gas ( = 1.5 ) undergoes an adiabatic compression. If the final pressure is 27 8 times the initial pressure and the initial volume is 27 L, the final volume of the gas is:

Step-by-step solution

For an adiabatic process, the relationship between pressure and volume is given by: P_i V_i^ = P_f V_f^ Rearranging for the final volume V_f : V_f = V_i ( P_i P_f )^ 1 Given that = 1.5 = 3 2 , the exponent becomes 1 = 2 3 . We are given V_i = 27 L and P_f P_i = 27 8 , which means P_i P_f = 8 27 . Substituting these values: V_f = 27 ( 8 27 )^ 2 3 V_f = 27 ( ( 2 3 )^3 )^ 2 3 = 27 ( 2 3 )^2 V_f = 27 4 9 = 12 L Answer: 12 L