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CER 126 Problem Set 3, Quizzes of Material Science and Technology

Bicol University (BU)Material Science and Technology

This is a problem set related to thermochemistry and thermodynamics.

Typology: Quizzes

2020/2021

Uploaded on 10/11/2022

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CER 126 : Thermodynamics of Materials May 13, 2022
Problem Set No. 3 Due : May 24, 2022
Name : ___________________________________________________
Answer the following ask questions.
1. You are responsible for the purchase of oxygen gas which, before use, will be stored at a
pressure of 200 atm at 300 K in a cylindrical vessel of diameter 0.2 m and height 2 m.
Would you prefer that the gas behaved ideally or as a van der Waals fluid? The van der
Waals constants for oxygen are a = 1.36 liters2 ・atm ・mole– 2 and b = 0.0318
liters/mole.
2. The virial equation of state for n -butane at 460 K is Z = 1 + A /V + B /V 2 , in which A =
– 265 cm3 /g ・mole and B = 30,250 cm6 /g ・mole2 . Calculate the work required to
reversibly compress 1 mole of n -butane from 50 to 100 atm at 460 K.
3. For sulfur dioxide, T cr = 430.7 K and P cr = 77.8 atm. Calculate
a. The critical van der Waals constants for the gas
b. The critical volume of van der Waals SO2
c. c. The pressure exerted by 1 mole of SO2 occupying a volume of 500 cm3 at 500
K. Compare this with the pressure which would be exerted by an ideal gas
occupying the same molar volume at the same temperature.
4. One hundred moles of hydrogen gas at 298 K are reversibly and isothermally compressed
from 30 to 10 liters. The van der Waals constants for hydrogen are a = 0.2461 liters2 ・
atm ・mole– 2 and b = 0.02668 liters/mole, and in the range of pressure 0– 1500 atm, the
virial equation for hydrogen is PV = RT (1 + 6.4 × 10– 4 P ). Calculate the work that
must be done on the system to effect the required change in volume and compare this
with the values that would be calculated assuming that (a) hydrogen behaves as a van der
Waals fluid and (b) hydrogen behaves as an ideal gas.
5. Using the virial equation of state for hydrogen at 298 K given in Problem 5, calculate
a. The fugacity of hydrogen at 500 atm and 298 K
b. The pressure at which the fugacity is twice the pressure
c. The change in the Gibbs free energy caused by a compression of 1 mole of hydrogen at
298 K from 1 to 500 atm
What is the magnitude of the contribution to (c) caused by the nonideality of hydrogen?
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CER 126 : Thermodynamics of Materials May 13, 2022

Problem Set No. 3 Due : May 24, 2022

Name : ___________________________________________________

Answer the following ask questions.

  1. You are responsible for the purchase of oxygen gas which, before use, will be stored at a pressure of 200 atm at 300 K in a cylindrical vessel of diameter 0.2 m and height 2 m. Would you prefer that the gas behaved ideally or as a van der Waals fluid? The van der Waals constants for oxygen are a = 1.36 liters^2 ・ atm ・ mole– 2^ and b = 0. liters/mole.
  2. The virial equation of state for n -butane at 460 K is Z = 1 + A / V + B / V 2 , in which A =
    • 265 cm3 /g ・ mole and B = 30,250 cm6 /g ・ mole2. Calculate the work required to reversibly compress 1 mole of n -butane from 50 to 100 atm at 460 K.
  3. For sulfur dioxide, T cr = 430.7 K and P cr = 77.8 atm. Calculate a. The critical van der Waals constants for the gas b. The critical volume of van der Waals SO 2 c. c. The pressure exerted by 1 mole of SO 2 occupying a volume of 500 cm^3 at 500 K. Compare this with the pressure which would be exerted by an ideal gas occupying the same molar volume at the same temperature.
  4. One hundred moles of hydrogen gas at 298 K are reversibly and isothermally compressed from 30 to 10 liters. The van der Waals constants for hydrogen are a = 0.2461 liters^2 ・ atm ・ mole– 2^ and b = 0.02668 liters/mole, and in the range of pressure 0– 1500 atm, the virial equation for hydrogen is PV = RT (1 + 6.4 × 10– 4 P ). Calculate the work that must be done on the system to effect the required change in volume and compare this with the values that would be calculated assuming that (a) hydrogen behaves as a van der Waals fluid and (b) hydrogen behaves as an ideal gas.
  5. Using the virial equation of state for hydrogen at 298 K given in Problem 5, calculate a. The fugacity of hydrogen at 500 atm and 298 K b. The pressure at which the fugacity is twice the pressure c. The change in the Gibbs free energy caused by a compression of 1 mole of hydrogen at 298 K from 1 to 500 atm What is the magnitude of the contribution to (c) caused by the nonideality of hydrogen?
  1. One mole of solid Cr 2 O 3 at 2500 K is dissolved in a large volume of a liquid Raoultian solution of Al 2 O 3 and Cr 2 O 3 , in which X (^) Cr2O3 = 0.2 and which is also at 2500 K. Calculate the changes in enthalpy and entropy caused by the addition. The normal melting temperature of Cr 2 O 3 is 2538 K, and it can be assumed that Δ Sm ,Al2O3 = Δ Sm ,Cr2O3.
  2. When 1 mole of argon gas is bubbled through a large volume of an Fe– Mn melt of X (^) Mn = 0.5 at 1863 K, the evaporation of Mn into the Ar causes the mass of the melt to decrease by 1.5 g. The gas leaves the melt at a pressure of 1 atm. Calculate the activity coefficient of Mn in the liquid alloy.
  3. The variation, with composition, of G XS^ for liquid Fe– Mn alloys at 1863 K is as follows: a. Does the system exhibit regular solution behavior? b. Calculate = 0.6. c. Calculate = 0.4. d. Calculate the partial pressures of Mn and Fe exerted by the alloy of X (^) Mn = 0.2.
  4. Calculate the heat required to form a liquid solution at 1356 K, starting with 1 mole of Cu and 1 mole of Ag at 298 K. At 1356 K, the molar heat of mixing of liquid Cu and liquid Ag is given by Δ HM^ = – 20,590 X (^) Cu X Ag.
  5. Melts in the system Pb– Sn exhibit regular solution behavior. At 473° C, a Pb = 0.055 in a liquid solution of X (^) Pb = 0.1. Calculate the value of α for the system and calculate the activity of Sn in the liquid solution of X Sn = 0.5 at 500° C.
  6. The activity coefficient of Zn in liquid Zn– Cd alloys at 435° C can be represented as Derive the corresponding expression for the dependence of ln γCd on composition and calculate the activity of cadmium in the alloy of X (^) Cd = 0.5 at 435° C.
  7. The molar excess Gibbs free energy of formation of solid solutions in the system Au– Ni can be represented by Calculate the activities of Au and Ni in the alloy of X Au = 0.5 at 1100 K.