Two moles of an ideal gas ( = 1.5 R) is subjected to the following changes in states: A (500 K, 5 bar) → Reversible Isothermal Expansion → B → Isochoric Cooling → C (250 K, 1 bar) → Single stage adiab

Question

Two moles of an ideal gas ($C_{v,m}$ = 1.5 R) is subjected to the following changes in states: A (500 K, 5 bar) → Reversible Isothermal Expansion → B → Isochoric Cooling → C (250 K, 1 bar) → Single stage adiabatic compression → D (3 bar). The correct statement(s) is/are:

Prashant Kotian · Accepted Answer

Correct answer: A,B,C. State A: T_A=500K, P_A=5bar, V_A=nRT_A/P_A=200R. B: isothermal so T_B=500K. C: isochoric from B, T_C=250K, P_C=1bar, V_C=nRT_C/P_C=500R=V_B. P_B=nRT_B/V_B=2*R*500/500R=2bar (A correct). D: adiabatic against P_ext=3bar; n**(T_D-250)=-3*(2/3*R*T_D-500R) => 3*(T_D-250)=-2T_D+1500 => 5T_D=2250 => T_D=450K (B correct). Δ H_CD=n**dT=2*2.5R*(450-250)=1000R (C correct). Δ U_BC=2*1.5R*(250-500)=-750R (D incorrect).

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