AE 2010 Thermodynamics (Problem Set #3: Gas State Equations, work and phase
change) NEW VERSION UPDATE WITH SOLUTION Georgia Institute Of
Technology
• Always indicate any assumptions you make. If you use any results or equations from
the class notes or text in you solutions, please note and reference them (but you
better be sure they are applicable to the problem at hand).
• Show all your work, no credit for just answers. When applicable, try to solve the
problem algebraically first. Only use numbers/values in the final steps of your solution
– and be sure to include units when you insert numbers.
• If the problem statement is given in ENGLISH units, the answer must also be in
English units; if the problem statement is in SI units, the answer must be in SI units.
1. Gas Storage
A small satellite being designed requires a nitrogen storage tank to store propellant
for the cold gas thruster used to maintain the satellite’s orientation. The
requirements call for 50.0 kg of N2 to be stored in a rigid container at 5°C and 65.0
bar when the satellite is deployed in space. Assuming that nitrogen is an ideal gas,
what is the minimum required size (i.e., volume) of the storage tank?
While the satellite awaits launch, it is estimated that the temperature in the tank
could reach as high as 45°C. If this happens, what will be the maximum internal
pressure that the storage vessel must be able to handle (again, assume nitrogen is
an ideal gas)?
2. Work and Energy
A closed vessel contains 10 lbm of an ideal gas with a molecular weight of 60.1
lbm/lbmole and a specific heat ratio of 1.23. The gas is initially at a pressure of 2.0
atm and a temperature of 140°F. The gas pressure is then tripled without changing
the density of the gas. Find the changes in internal energy, U, and enthalpy, H, of
the gas, during this process AND the amount of work done to the gas. You MUST
include a sketch of the process on a p-v diagram.
3. Ideal Gases – Internal Energy and Enthalpy
Consider a process that takes an ideal gas between an initial state (350.K, 1.0 atm)
and a final state (1000. K, 10.0 atm). Calculate the specific enthalpy and internal
energy changes (i.e., per unit mass) for such a process for two substances: H 2 and
H2O. Calculate your answer using the following three different approaches:
(a) assume the specific heats are constants (i.e., the calorically perfect gas
assumption) - and use a ROOM TEMPERATURE value for the specific heats;
(b) allow the specific heat to vary with temperature and use the polynomial
expressions for specific heats found in Table D.11;
, (c) use the tabulated values for u and h of the gases found in the appropriate Tables
in your text (D.4 and D.7)
4. Water - Energy Change and Work
0.50 lbm of water is contained in a closed piston-cylinder system initially at 300. F
and 500. psia. If the water is heated at constant pressure:
(a) what is the final temperature if the final volume is 0.40 ft3;
(b) what is the enthalpy change (i.e., final minus initial) of the water if the final
volume is 0.40 ft3;
(c) what is the enthalpy change if the final temperature is 600. F;
(d) how much work is done if the final temperature is 600. F.
,
change) NEW VERSION UPDATE WITH SOLUTION Georgia Institute Of
Technology
• Always indicate any assumptions you make. If you use any results or equations from
the class notes or text in you solutions, please note and reference them (but you
better be sure they are applicable to the problem at hand).
• Show all your work, no credit for just answers. When applicable, try to solve the
problem algebraically first. Only use numbers/values in the final steps of your solution
– and be sure to include units when you insert numbers.
• If the problem statement is given in ENGLISH units, the answer must also be in
English units; if the problem statement is in SI units, the answer must be in SI units.
1. Gas Storage
A small satellite being designed requires a nitrogen storage tank to store propellant
for the cold gas thruster used to maintain the satellite’s orientation. The
requirements call for 50.0 kg of N2 to be stored in a rigid container at 5°C and 65.0
bar when the satellite is deployed in space. Assuming that nitrogen is an ideal gas,
what is the minimum required size (i.e., volume) of the storage tank?
While the satellite awaits launch, it is estimated that the temperature in the tank
could reach as high as 45°C. If this happens, what will be the maximum internal
pressure that the storage vessel must be able to handle (again, assume nitrogen is
an ideal gas)?
2. Work and Energy
A closed vessel contains 10 lbm of an ideal gas with a molecular weight of 60.1
lbm/lbmole and a specific heat ratio of 1.23. The gas is initially at a pressure of 2.0
atm and a temperature of 140°F. The gas pressure is then tripled without changing
the density of the gas. Find the changes in internal energy, U, and enthalpy, H, of
the gas, during this process AND the amount of work done to the gas. You MUST
include a sketch of the process on a p-v diagram.
3. Ideal Gases – Internal Energy and Enthalpy
Consider a process that takes an ideal gas between an initial state (350.K, 1.0 atm)
and a final state (1000. K, 10.0 atm). Calculate the specific enthalpy and internal
energy changes (i.e., per unit mass) for such a process for two substances: H 2 and
H2O. Calculate your answer using the following three different approaches:
(a) assume the specific heats are constants (i.e., the calorically perfect gas
assumption) - and use a ROOM TEMPERATURE value for the specific heats;
(b) allow the specific heat to vary with temperature and use the polynomial
expressions for specific heats found in Table D.11;
, (c) use the tabulated values for u and h of the gases found in the appropriate Tables
in your text (D.4 and D.7)
4. Water - Energy Change and Work
0.50 lbm of water is contained in a closed piston-cylinder system initially at 300. F
and 500. psia. If the water is heated at constant pressure:
(a) what is the final temperature if the final volume is 0.40 ft3;
(b) what is the enthalpy change (i.e., final minus initial) of the water if the final
volume is 0.40 ft3;
(c) what is the enthalpy change if the final temperature is 600. F;
(d) how much work is done if the final temperature is 600. F.
,
