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