One mole of a monoatomic ideal gas at $400 K$ and $5.00 bar$ expands irreversibly and adiabatically against a constant external pressure of $1.00 bar$ until the gas reaches mechanical equilibrium with the surroundings. Find the final temperature in $K$ (nearest integer).

Numerical answer type, answer in K, tolerance 0.5.

Answer: 272 K

With

q = 0

n C_{v} (T_{2} - T_{1}) = - P_{e x t} (V_{2} - V_{1})

and

V = RT / P

. So

\frac{3}{2} R (T_{2} - T_{1}) = - R (T_{2} - P_{e x t} T_{1} / P_{1})

, giving

2.5 T_{2} = (1.5 + 0.2) \times 400 = 680

, i.e.

T_{2} = 272 K