ECHE 311/FALL 2003
Problem Set #1
Due Friday August 29
1. A container filled with 30 kg of water at 20oC is fitted with a stirrer, which is made to turn
by gravity acting on a weight of mass 60 kg. The weight falls through a distance of 15 m in
driving the stirrer. Assuming that all work done on the weight is transferred to the water and
that the local acceleration of gravity is 9.8 ms-2, determine:
(a) The amount of work done on the water.
(b) The internal energy change of the water
(c) The final temperature of the water, for which Cp=4.18 kJ kg-1 oC
2. (a) Three moles of nitrogen at 30oC, contained in a rigid vessel, is heated to 250oC. How
much heat is required if the vessel has a negligible heat capacity? If the vessel weighs 100
kg and has a heat capacity of 0.5 kJ kg-1oC-1, how much heat is required?
(b) Four moles of nitrogen at 200oC is contained in a piston/cylinder arrangement. How
much heat must be extracted from the system, which is kept at constant pressure, to cool it
40oC if the heat capacity of the piston and cylinder is neglected. Take Cv=20.8 and CP=29.1
J mol-1 o C for nitrogen gas.
3. An ideal gas, CP= (5/2)R and CV=(3/2)R is changed from P1=1 bar and V1t=12 m3 to P2=12
bar and V2t =1 m3 by the following mechanically reversible processes:
(a) Isothermal compression.
(b) Adiabatic compression followed by cooling at constant pressure
(c) Adiabatic compression followed by cooling at constant volume.
Calculate Q, W,  Ut, and  Ht for each process for each of these processes, and sketch the
paths of all processes on a single PV diagram.
Hint: for all part of this problem T2=T1 and  U=  H=0 Also Q=-W. Thus, it remains to
calculate W. Use symbol V for total volume in this problem.
4. One cubic meter of an ideal gas at 600 K and 1,000 kPa expands to five times its initial
volume as follows:
(a) By a mechanically reversible, isothermal process
(b) By a mechanically reversible adiabatic process
For each case calculate the final temperature, pressure and the work done by the gas, C p=21
J mol-1K-1.
5. One kilogram of air is heated reversibly at constant pressure from an initial state of 300 K
and 1 bar until its volume triples. Calculate W, Q,  U, and  H for the process. Assume
that air obeys the relation PV/T=83.14 bar cm3 mol-1 K-1 and that Cp=29 J mol-1 K-1.
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6. A steel casting weighing 2 kg has an initial temperature of 500oC; 40 kg of water initially at
25oC is contained in a perfectly insulated steel tank weighing 5 kg. The casting is immersed
in the water and the system is allowed to come to equilibrium. What is the final
temperature? Ignore any effect of expansion or contraction, and assume constant specific
heats of 4.18 kJ kg-1K-1 for water and 0.50 kJ kg-1K-1 for steel.
7. The conditions of a gas change in a steady-flow process from 20oC and 1,000 kPa to 60oC
and 100 kPa. Devise a reversible nonflow process (any number of steps) for accomplishing
this change of state, and calculate U and H for the process on the basis of 1 mol of gas.
Assume for the gas that PV/T is constant, CV = (5/2)R and CP=(7/2)R.
8. With respect of 1 kg of liquid water:
i. Initially at 0oC, it is heated to 100oC by contact with a heat reservoir at
100oC. What is the entropy change of the water? Of the heat reservoir? What
is Stotal .
ii. Initially at 0oC, it is first heated to 50oC by contact with a heat reservoir at
50oC and then to 100oC by contact with a reservoir at 100oC. What is
Stotal .
iii. Explain how the water might be heated from 0oC to 100oC so that Stotal =0.
Take the heat capacity of water to be constant at the value: Cp=4.184 kJ/kg K.
9. One mole of ideal gas, Cp=(7/2)R and CV=(5/2)R is compressed adiabatically in a
piston/cylinder device from 2 bar and 25oC to 7 bar. The process is irreversible and requires
35% more work than a reversible adiabatic compression from the same initial state to the
final pressure. What is the entropy change of the gas?
Hint: W  U  Cv (T2-T1) Whence T2  T1 
W
CV
T
P
and S  C P ln( 2 )  R ln( 2 )
T1
P1
10. A reversible cycle executed by 1 mol of an ideal gas for which Cp= (5/2)R and CV=(3/2R)
consists of the following:
(i)
Starting at T1=700 K and P1=1.5 bar, the gas is cooled at constant pressure to
To=350K.
(ii)
From 350 K and 1.5 bar, the gas is compressed isothermally to pressure P2.
(iii)
The gas returns to its initial state along the path which product the PT is constant.
What is the thermal efficiency of the cycle
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ECHE 311/FALL 2002
Problem Set 2
Due September 5th
1. What is the heat required when 12 mol of propane is heated from 250 to 1,200 oC at
approximately atmospheric pressure in a steady state-flow heat exchanger?
 Use equation 4. 7 which approximate the heat capacity and calculates ICPH.
 H  R  ICPH
 Q(n)  nH ( n is number of moles)
2. What is the final temperature when heat in the amount of 800 kJ is added to the 10 mol of
ethylene initially at 200oC in a steady-flow heat exchanger at approximately atmospheric
pressure?
Hint :
T
 2 (guess)
 Use  
To
in equation
B
C
Q  nR{[ ATo (  1)  To2 ( 2  1)]  To3 ( 3  1)}
(1)
2
3
to estimate the best value for  and the final temperaure
3. Chlorine is produced by the reaction
4HCl(g) + O2(g) = 2H2O(g) +2Cl2(g)
The feed stream to the reactor consists of 60% HCl, 36 mol% O2 and 4 mole % N2, and it
enters the reactor at 550oC. If the conversion of HCl is 75% and if the process is isothermal,
how much heat must be transferred from the reactor per mole of the entering gas mixture?
Hint:
 Take a basis of 1 mole gas entering reactor, containing 0.6 M HCl, 0.36 M O2 and
0.04 M N2. Therefore the amount of HCl reacted (r) is equal to 0.6x0.7=0.45.
 Using H298 as the reference, we can calculate H823 by the equation
H 823  H 298  MDCPH  R  (T  T298 )
B
C
D
MDCPH  A  ( ) T o(  1)  (
)  To2 ( 2    1) 
2
3
  To2
T
where To=298.15 K ;  
To
3
(2)
4. If the heat of the amount of 2,500 kJ is added to 15 mol of 1 butene initially at 260 oC in a
steady state-flow process at approximately atmospheric pressure, what is its entropy change?
T
 3 as a guess value in Eq 1 to calculate the final temperature.
 Use  
To
 The entropy for 15 moles is the found by using Eq. 5.15 (ICPS integral)
 S  nR  ICPS
5. Calculate the reversible work done on compressing 1 ft3 of mercury at a constant
temperature of 32(oF) from 1 atm to 3,000 (atm). The isothermal compressibility of mercury
at 32oF is
=3.9x10-6-0.1x10-9P
-1
where P is in (atm) and  is in (atm) .

6. Five kilograms of liquid carbon tetrachloride undergo a mechanically reversible, isobaric
change of state at 1 bar during which the temperature changes from 0oC to 20. Determine
Vt, W, Q, Ht, and Ut. The following parameters for liquid carbon tetrachloride at 1 bar
and 0oC may be assumed independent of temperature:  =1.2x10-3 K-1, CP =0.84 kJ kg-1K-1,
and
=1.590 kg m-3.

7. Values for the latent heats of vaporization in J g-1 are given in the following table for a
number of pure liquids at 25oC and Tn, the normal boiling point (see App. B in SVNA for B
values).
Hiv at 25oC
n-Pentane
n-Hexane
366.3
3.66.1
Hiv at Tn
357.2
336.7___
For these substances calculate:
(a) the value of the latent heat at Tn by Eq. (4.19), given the value at 25oC.
(b) the value of the latent heat at Tn by Eq. (4.18).
By what percentage do these values differ from the one listed in table ?
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