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One mole of a monoatomic ideal gas undergoes an irreversible adiabatic expansion against a constant external pressure of 1 atm. The initial conditions are: pressure = 5 atm and temperature = 300 K. The process continues until the gas pressure equals 2 atm. What is the final temperature (in K)? (R = 2 cal / mol K)

1. 270 K
2. 250 K
3. 240 K
4. 260 K

Correct answer: 270 K

Solution

In an irreversible adiabatic expansion against constant P_ext, q = 0 so delta U = -w. Work done by gas = P_ext*(V_f - V_i). Using ideal gas law and Cv = (3/2)R, we solve for T_f.

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