A sample of a non-linear polyatomic ideal gas undergoes a reversible adiabatic compression. If this process causes the absolute temperature of the gas to become exactly 3 times its initial value, the ratio of the final pressure to the initial pressure is:

Step-by-step solution

For a non-linear polyatomic ideal gas, the ratio of specific heats is = 4 3 . In a reversible adiabatic process, the relationship between temperature T and pressure P is given by: T^ P^ 1- = constant This can be rearranged as: P T^ -1 Let us calculate the exponent: -1 = 4 3 4 3 - 1 = 4 3 1 3 = 4 Therefore, P T^4 . Given that the final temperature is 3 times the initial temperature ( T₂ = 3T₁ ), the ratio of final to initial pressure is: P₂ P₁ = ( T₂ T₁ )^4 = (3)^4 = 81 Answer: 81