One mole of an ideal monoatomic gas at 27°C is subjected to a reversible isoentropic compression until the final temperature reached 327°C. If the initial pressure was 1 atm then, find the value of final pressure.
Correct answer: A. 0.75 atm
- A. 0.75 atm
- B. 2 atm
- C. 2.5 atm
- D. 0.5 atm
Explanation
In an adiabatic process for an ideal monoatomic gas, the relationship between pressure and temperature is given by the equation: P1/T1^(γ/(γ-1)) = P2/T2^(γ/(γ-1)), where γ (gamma) is the heat capacity ratio (Cp/Cv) and is 5/3 for a monoatomic gas. Given the initial temperature (T1 = 27°C = 300K) and final temperature (T2 = 327°C = 600K), and knowing that the initial pressure (P1) is 1 atm, solving for P2 gives us 0.75 atm. The other options do not satisfy this relationship based on the given temperatures and initial conditions.
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