A gas has a constant-pressure ideal-gas heat capacity of

Question

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.

Liquid	MW	ρ(g/cm3)	103αP(K-1)	106κT(bar-1)
(a) Acetone	58.08	0.7899	1.487	111
(b) Ethanol	46.07	0.7893	1.12	100
(c) Benzene	78.12	0.87865	1.237	89
(d) Carbon disulfide	76.14	1.258	1.218	86
(e) Chloroform	119.38	1.4832	1.273	83
(f) Ethyl ether	74.12	0.7138	1.656	188
(g) Mercury	200.6	13.5939	0.18186	3.95
(h) Water	18.02	0.998	0.207	49

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.