AE 2010 Thermodynamics (PROBLEM SET #2: WORK, PATHS, AND IDEAL GAS
LAW) WITH SOLUTION Georgia Institute Of Technology
Problem Set #2: Work, Paths, and ideal gas law
• 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. Work and Paths
A simple compressible substance of fixed mass undergoes an increase in both
pressure (p) and specific volume (v) from state 1 (p1, v1) to state 2 (p2, v2). Two ways
to accomplish this are being considered. In the first case (path A), the overall path is
a constant pressure (isobaric) process followed by a constant-volume (isochoric)
process. In the second case (path B), the pressure rises as the square-root of the
2
volume increase, i.e., p v1 .
Determine: (a) is there net work being done in path (A) to the substance or by the
substance on its surroundings; (b) same question as (a) for path (B); (c) which path
involves the largest (absolute value) amount of work; and (d) will the change in
internal energy be greater for path A than for path B. As part of your answer, you
MUST also draw the two paths on a p-v diagram.
2. Expansion Work
A pneumatic “blaster” is a device that launches a low mass projectile from a
cylindrical tube using pressurized air stored upstream of the projectile. The projectile
is held in place while the pressurized air is introduced to the cylinder. After the
trigger is released, the projectile accelerates down the tube, while the pressure
upstream of the projectile drops according to the relation,
(x d )2
p = pi 1 −
30
where pi is the initial (high) pressure in the tube before the trigger is release, x is the
distance traveled by the projectile and d is the diameter of the tube. If we have a
5.0 cm diameter tube, with a projectile initially located 5.0 tube diameters upstream
of the tube exit, and the initial pressure upstream of the projectile is 1.2 MPa,
determine the work done by the air on the projectile during the time that projectile is
in the tube, assuming there is no friction between the tube and the projectile.
, 3. Enthalpy
First, determine the specific enthalpy of the following two substances at the given
conditions. Then identify which of the substances is likely to be a gas. Finally, for the
substance that is likely to be a gas, determine if it can be considered a calorically
perfect gas over the range 300-1000 K
Substance p (bar) T (K) (kg/m3) u (kJ/kg)
A 1.00 300. 1.20 0.00
A 20.0 300. 24.0 0.50
A 20.0 500. 14.0 110
A 20.0 1000. 7.20 440
B 1.00 300. 500 0.00
B 20.0 300. 505 1.00
B 20.0 500. 501 220
B 20.0 1000. 490 810
LAW) WITH SOLUTION Georgia Institute Of Technology
Problem Set #2: Work, Paths, and ideal gas law
• 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. Work and Paths
A simple compressible substance of fixed mass undergoes an increase in both
pressure (p) and specific volume (v) from state 1 (p1, v1) to state 2 (p2, v2). Two ways
to accomplish this are being considered. In the first case (path A), the overall path is
a constant pressure (isobaric) process followed by a constant-volume (isochoric)
process. In the second case (path B), the pressure rises as the square-root of the
2
volume increase, i.e., p v1 .
Determine: (a) is there net work being done in path (A) to the substance or by the
substance on its surroundings; (b) same question as (a) for path (B); (c) which path
involves the largest (absolute value) amount of work; and (d) will the change in
internal energy be greater for path A than for path B. As part of your answer, you
MUST also draw the two paths on a p-v diagram.
2. Expansion Work
A pneumatic “blaster” is a device that launches a low mass projectile from a
cylindrical tube using pressurized air stored upstream of the projectile. The projectile
is held in place while the pressurized air is introduced to the cylinder. After the
trigger is released, the projectile accelerates down the tube, while the pressure
upstream of the projectile drops according to the relation,
(x d )2
p = pi 1 −
30
where pi is the initial (high) pressure in the tube before the trigger is release, x is the
distance traveled by the projectile and d is the diameter of the tube. If we have a
5.0 cm diameter tube, with a projectile initially located 5.0 tube diameters upstream
of the tube exit, and the initial pressure upstream of the projectile is 1.2 MPa,
determine the work done by the air on the projectile during the time that projectile is
in the tube, assuming there is no friction between the tube and the projectile.
, 3. Enthalpy
First, determine the specific enthalpy of the following two substances at the given
conditions. Then identify which of the substances is likely to be a gas. Finally, for the
substance that is likely to be a gas, determine if it can be considered a calorically
perfect gas over the range 300-1000 K
Substance p (bar) T (K) (kg/m3) u (kJ/kg)
A 1.00 300. 1.20 0.00
A 20.0 300. 24.0 0.50
A 20.0 500. 14.0 110
A 20.0 1000. 7.20 440
B 1.00 300. 500 0.00
B 20.0 300. 505 1.00
B 20.0 500. 501 220
B 20.0 1000. 490 810
