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Two moles of an ideal gas with Cv,m = (3/2)R undergo the following sequence of processes: A (500 K, 5.0 bar) -> B via reversible isothermal expansion -> C (250 K, 1.0 bar) via irreversible cooling -> D via single-stage adiabatic compression to 3 bar. Which of the following statements are CORRECT?

1. The pressure at state B is 2.0 bar
2. The temperature at state D is 450 K
3. Delta_H for process C to D equals 1000 R
4. Delta_U for process B to C equals -375 R

Correct answer: The pressure at state B is 2.0 bar

Solution

A->B is isothermal at 500 K; B->C brings T to 250 K, 1 bar; assuming B->C is at constant pressure (isobaric), P_B = 1.0 bar contradicts option A. If B->C is at constant volume, then P_B/T_B = P_C/T_C gives P_B = (500/250)*1.0 = 2.0 bar, confirming option A. For D: single-stage adiabatic compression to 3 bar with P_ext = 3 bar gives T_D via work-energy balance.

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