One cubic meter of argon is taken from 1 bar and 25°C to 10 bar and 300°C by each of the following two-step paths. For each path, compute Q, W, ?U, and ?H for each step and for the overall process. Assume mechanical reversibility and treat argon as an ideal gas with 
and 
What will be an ideal response?
(a) Isothermal compression followed by isobaric heating.
(b) Adiabatic compression followed by isobaric heating or cooling.
(c) Adiabatic compression followed by isochoric heating or cooling.
(d) Adiabatic compression followed by isothermal compression or expansion.
a. Argon goes from 1 bar and 25 C isothermally compressed to 10 bar, and isobaric heating to 300 C. First, the volume at the initial state ( 
bar and 
25 C) is the 
(from V = RT/P). The volume at the final state 
10 bar and 
300 C)is the 
So for the isothermal compression, ?U = 0, Q = 
= -5707 J/mol,
W = -Q = -(-5707 J/mol) = 5707 J/mol, and ?H =0.
For the isobaric heating, ?U = Cv?T = 1.5* R * (573.15 K – 298.15 K) = 3429 J/mol,
?H = Q = Cp?T = 2.5* R * (573.15 K – 298.15 K) = 5715 J/mol,
W = -R?T = R * (573.15 K – 298.15 K) = -2286 J/mol.
Altogether, W =5707 J/mol – 2286 J/mol = 3421 J/mol, ?U =3429 J/mol, Q = -5707 J/mol + 5715 J/mol = 8 J/mol, ?H = 5715 J/mol.
b. Argon goes from 1 bar and 25 C adiabatically compressed to 10 bar, and isobaric heating to 300 C. Use the same volumes as in part (a).
So for the adiabatic compression, Q = 0,
For the isobaric heating,
?H = Q = 4930.26 J/mol,
Altogether,
W =-1972.11 J/mol +471.366 J/mol = -1500.74 J/mol,
?U =471.366 J/mol + 2958.16 J/mol = 3429.52 J/mol,
Q = 4930.26 J/mol,
?H = 4930.26 J/mol + 942.732 J/mol = 5873 J/mol.
c. Argon goes from 1 bar and 25 C adiabatically compressed to 10 bar, and isochoric heating to 300 C. Use the same volumes as in part (a).
So for the adiabatic compression, Q = 0,
For the isochoric heating,
Altogether, W =471.366 J/mol,
?U =471.366 J/mol + 2958.16 J/mol = 3429.52 J/mol,
?H = 4930.26 J/mol + 942.732 J/mol = 5873 J/mol.
Q = 2958.16 J/mol.
d. Argon goes from 1 bar and 25 C adiabatically compressed to 300C, and isothermal compression to 10 bar.
Use the same volumes as in part (a).
So for the adiabatic compression, Q = 0,
For the isothermal compression, ?H = ?U = 0,
Q = 
= -5707 J/mol, and W = -Q = 5707 J/mol
Altogether, W =471.366 J/mol + 5707 J/mmol = 6179.056 J/mol, ?U =471.366 J/mol, Q = -5707J/mol, ?H = 942.732 J/mol.
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