A monoatomic ideal gas is suddenly compressed such that its final pressure becomes 32 times its initial pressure. The ratio of the final volume to the initial volume of the gas is:

Step-by-step solution

The word 'suddenly' indicates that the compression is an adiabatic process. For an adiabatic process, the equation of state is: P_i V_i^ = P_f V_f^ For a monoatomic gas, the ratio of specific heats is = 5 3 . Given that P_f = 32 P_i , we can substitute this into the equation: P_i V_i^ 5 3 = 32 P_i V_f^ 5 3 ( V_f V_i )^ 5 3 = 1 32 Taking the power of 3 5 on both sides: V_f V_i = ( 1 32 )^ 3 5 = ( ( 1 2 )^5 )^ 3 5 = ( 1 2 )^3 = 1 8 Thus, the ratio of the final volume to the initial volume is 1 8 . Answer: 1 8