ECHE 311/SPRING 2011
Problem Set #1
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, Cp=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.
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