Q1. Express in terms of P, V, T, C_P, C_V, and their derivatives. Your answer may include absolute values of S if it is not a derivative constraint or within a derivative.

a. (∂G/∂P)_T

b. (∂P/∂A)_V

c. (∂T/∂P)_S

d. (∂H/∂T)_U

e. (∂T/∂H)_S

f. (∂A/∂V)P

g. (377/8P)_H

h. (∂A/∂S)_P

i. (∂S/∂P)_G

Q2.

 a. Derive (∂H/∂P)_T and (∂U/∂P)_T in terms of measurable properties.

b. dH = dU + d(PV) from the definition of H. Apply the expansion rule to show the difference between (∂H/∂P)_T and (∂U/∂P)_T is the same as the result from part (a).

Q3. Express (∂H/∂V)_T in terms of α_p and/or κ_T.

Q4. Determine the difference C_P - C_V for the following liquids using the data provided near 20°C.

Q5. A rigid container is filled with liquid acetone at 20°C and 1 bar. Through heat transfer at constant volume, a pressure of 100 bar is generated. C_P = 125 J/mol-K. (Other properties of acetone are given in Q4) Provide your best estimate of the following:

a. The temperature rise

b. ΔS, ΔU, and ΔH

c. The heat transferred per mole

Q6. The Soave-Redlich-Kwong equation is presented in Q7. Derive expressions for the enthalpy and entropy departure functions in terms of this equation of state.

Q7. The Soave-Redlich-Kwong equation is given by:

P = (RTρ/1-bρ) - (aρ²/1+bρ) or Z = (1/1-bρ) - (a/bRT) · (bρ/1+bρ)

where ρ = molar density = n/V 

a ≡ a_ca;   a_c ≡ 0.42748(R²T²c/P_c),                  b ≡ 0.08664(RT_c/P_c)

a ≡ [1 + κ(1 - √(T_r))]²            κ ≡ 0.480 + 1.574ω - 0.176ω²                                  

T_c, P_c, and ω are reducing constants according to the principle of corresponding.

Q8. A gas has a constant-pressure ideal-gas heat capacity of 15R. The gas follows the equation of state,

Z = 1 + aP/RT

over the range of interest, where a = -1000 cm³/mole,

a. Show that the enthalpy departure is of the following form:

(H - H^ig/RT) = aP/RT

b. Evaluate the enthalpy change for the gas as it undergoes the state change:

T₁ = 300 K, P₁ = 0.1 MPa, T₂ = 400 K, P₂= 2 MPa.