Reference no: EM131239884
Q1. Express in terms of P, V, T, CP, CV, 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 αp and/or κT.
Q4. Determine the difference CP - CV for the following liquids using the data provided near 20°C.
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Liquid
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MW
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ρ(g/cm3)
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103αP(K-1)
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106κT(bar-1)
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(a) Acetone
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58.08
|
0.7899
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1.487
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111
|
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(b) Ethanol
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46.07
|
0.7893
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1.12
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100
|
|
(c) Benzene
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78.12
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0.87865
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1.237
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89
|
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(d) Carbon disulfide
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76.14
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1.258
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1.218
|
86
|
|
(e) Chloroform
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119.38
|
1.4832
|
1.273
|
83
|
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(f) Ethyl ether
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74.12
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0.7138
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1.656
|
188
|
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(g) Mercury
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200.6
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13.5939
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0.18186
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3.95
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(h) Water
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18.02
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0.998
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0.207
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49
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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. CP = 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 ≡ aca; ac ≡ 0.42748(R2T2c/Pc), b ≡ 0.08664(RTc/Pc)
a ≡ [1 + κ(1 - √(Tr))]2 κ ≡ 0.480 + 1.574ω - 0.176ω2
Tc, Pc, 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 - Hig/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.
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