Page 110 - Advanced thermodynamics for engineers

4.12 PROBLEMS 95

(a) When the air follows path 1-a-2, see Fig. P4.2(b), calculate the following work output
quantities in each of the subprocesses 1-a and a-2.
, coming from the control volume as the air passes through the
(i) The direct shaft work, W x A
given subprocess.
(ii) The external work, W e , produced by any auxiliary cyclic devices required to ensure
external reversibility in that exchange with the environment during the given subprocess.
(iii) The gross work, W g .
(iv) The total useful shaft work, W x .
[66.03; 62.2; 128.23; 128.23 (kJ/kg)]
(b) Calculate the above work output quantities for each of the subprocesses 1-b and b-2 when the
air follows the alternative path 1-b-2.
[109.41; 18.77; 128.18; 128.18 (kJ/kg)]
P4.3 Confirm that item (iv) in P4.2 is equal to (b 1 b 2 ), where b ¼ h T 0 s, the specific steady-flow
availability function. (Note that, since T 2 ¼ T 0 and p 2 ¼ p 0 , state 2 is the dead state, so that
item (iv) is in this case equal to the steady-flow exergy of unit mass of air in state 1 for an
environment at T 0 ¼ 300 K and p 0 ¼ 1 bar.)
[128.2 kJ/kg]
P4.4 A mass of 0.008 kg of helium is contained in a piston-cylinder unit at 4 bar and 235 C. The

piston is pushed in by a force, F, until the cylinder volume is halved, and a cooling coil is used
to maintain the pressure constant. If the dead-state conditions are 1.013 bar and 22 C,

determine:
(i) The work done on the gas by the force, F;
(ii) The change in availability;
(iii) The heat transfer from the gas and
(iv) The irreversibility.
Show the heat transfer process defined in part (iii) and the unavailable energy on a T–s
diagram, and the work terms on a p–V diagram.
The following data may be used for helium, which can be assumed to behave as a perfect gas:

Ratio of specific heats, k ¼ c p /c v ¼ 1.667
Molecular weight, m w ¼ 4
Universal gas constant, <¼ 8.3143 kJ/kmol K.
[ 3.154 kJ; 1.0967 kJ; 10.556 kJ; 2.0573 kJ]
P4.5 A system at constant pressure consists of 10 kg of air at a temperature of 1000 K. Calculate the
maximum amount of work which can be obtained from the system if the dead-state
temperature is 300 K, and the dead-state pressure is equal to the pressure in the system. Take
the specific heat at constant pressure of air, c p , as 0.98 kJ/kg K (see P2.8, Chapter 2).
[3320.3 kJ]
P4.6 A thermally isolated system at constant pressure consists of 10 kg of air at a temperature of
1000 K and 10 kg of water at 300 K, connected together by a reversible heat engine. What is
the maximum work that can be obtained from the system as the temperatures equalise? (See
P2.9, Chapter 2.)