Review problems

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Show that CP-CV = β2VT/κ for any material

A sample of gas initially occupies a volume of 1 liter under a pressure of 1

atm. The gas is reversibly taken through the following cycle:

Heated at constant volume until P=2 atm

Heated at constant pressure until V=2 liters

Cooled at constant volume until P=1 liter

Cooled at constant pressure until V=1 liter

Calculate the total change in internal energy, heat and work for the

complete cycle

One mole of a gas initially at 100 °C and 10 atm, is subjected to the

following sequence:

a. Adiabatic expansion until pressure is reduced to 5 atm

b. Isobaric volume change until temperature becomes 100 °C

c. Isothermal volume change until pressure becomes 10 atm

Schematically plot above processes on P-V diagram and compare the work

produced in each path

Two moles of an ideal gas at 3 atm and 300 K in a cylinder fitted with a

piston is compressed isothermally to half of the initial volume by an

external pressure of 7 atm. Find the change in internal energy,heat and

work

An aircraft turbofan adiabatically and reversibly compresses air from an

initial state of 0.9 atm and 298 K to 9 atm just prior to admission to the

combustion chamber. Determine the temperature of air at the entrance of

the combustion chamber

(Assume air is a mixture of 21% O2 and 79% N2 by volume)

CV(N2(g)) = 31.8 J/mole.K

CV(O2(g)) = 33.5 J/mole.K

Liquid copper at 1150 °C is being poured into a water cooled continous

casting mould. Mould has 0.02m3 of volume. The casting rate is 10 cm3/s.

Calculate the minimum flow rate of water entering at 15 °C, required to

yield a discharge temperature of 80 °C. The average temperature at the

bottom of the mould is 1083 °C and copper is in solid state

Cp(Cu(l)) = 31.3 J/mole.K

ΔHm(Cu) = 13000 J/mole at Tm = 1083 °C, density = 8g/cm3 AW=63.5 gr/mol

CP(H2O(l)) = 75.47 J/mole.K

Most real gases obey the following equation of state:

PV = nRT + bP

Find an expression for work when the gas undergoes a reversible

isothermal volume change

Calculate the isothermal enthalpy change at 1000K for the process

Pb(l) + CO2(g) = PbO(s) + CO(g)

CO(g) ΔH298=-110510 J/mol Cp= 28.42 + 0.0041T – 46000/T2 J/molK

CO2(g) ΔH298=-394000 J/mole, Cp=44.3+0.0088T-860000/T2 J/molK

PbO(s) ΔH298=-219350 J/mole, Cp=37.9+0.0268T J/molK, HT-H298= -3508

+ 28.46T J/mol

Develop a relationship for the variation of enthalpy with pressure as a

function of β, T and V for isothermal processes and show that enthalpy

change with P for ideal gases is zero

Calculate the maximum flame temperature that could be attained when

CO(g) at 2000 C is used in combustion with air. Air is admitted at room

temperature. The combustion is carried out at 1 atm.

CO(g) ΔH298=-111000 J/mole, Cp=28.4+0.0041T J/molK

CO2(g) ΔH298=-394000 J/mole, Cp=44.3+0.0088T-860000/T2 J/molK

O2(g) Cp=29.97+0.00419T-167000/T2 J/moleK

N2(g) Cp=27.88+0.00427T J/molK

Hematite (Fe2O3) is reduced to metallic iron by carbon and the resulting

gaseous reaction product is a mixture of CO and CO2 with two parts of CO

to one part of CO2. Calculate the heat of this reaction per mole of Fe

produced at 25 C and 1000 K

Fe2O3(s) ΔH298=-821710 J/mole, (HT-H298)= -37758 + 98.3T + 0.03893T2

+ 1490000 J/mole

Fe(l) (HT-H298)= -754 + 41.9T J/mole

CO(g) ΔH298=-111000 J/mole, Cp=28.4+0.0041T J/molK

CO2(g) ΔH298=-394000 J/mole, Cp=44.3+0.0088T-860000/T2 J/molK

An adiabatic vessel contains 1000 grams of liquid aluminum at 700 C.

Calculate the weight of Cr2O3 which raises the temperature of the resulting

mixture of Al2O3(s), Cr(s) and Cr2O3(s) to 1000 C when added to the liquid

aluminum. The initial temperature of Cr2O3 is 25 C

Al2O3(s) H298=-1674400 J/mol, HT-H298=115.1T + 0.0059T2 + 3500000/T

J/mol

Al(s) HT-H298=-6719 + 20.68T + 0.0062T2 J/mol

Al(l) HT-H298= 1381 + 29.30T J/mol

Cr2O3(s) H298=-1130000 J/mol Cp=119.43 + 0.07535T J/molK

Cr2(s) Cp=23.35 J/molK

In an installation for the electric smelting of zinc, a gas mixture containing

45% Zn vapor and 55% CO gas by volume is passed into a condenser. The

gases enter the condenser at 950 C. The zinc gas condenses and cools down

to 600 C and the CO leaves the condenser at 600 C. How much heat per

mole of Zn must be removed from the condenser to keep the temperature

of the condenser constant? Midterm

CO(g) Cp= 28.42 + 0.0041T – 46000/T2 J/molK

Zn(s) Cp=22.4 + 0.01005 J/molK, ΔHm= 7388 J/mole at 693K,

Zn(l) Cp= 31.4 J/molK, ΔHv= 115350 J/mole at 1181K

Zn(g) Cp=20.76 J/molK

The normal freezing point for pure copper is 1083 C but small droplets of

liquid copper have been supercooled to 847 C before spontaneous

solidification occurs. Calculate the enthalpy change for the spontaneous

solidification of copper at 847 C and the ratio of solid residue if the

supercooled liquid was transferred to an adiabatic vessel at the same

temperature

Cu(s) S298=33.36 J/molK, Cp=22.65+0.00628T J/molK ΔHm= 13000

J/mole at 1356K

Cu(l) Cp= 31.40 J/molK