UNIVERSITY of PLYMOUTH

 

SCHOOL of ENGINEERING

 

BENG2 APPLIED THERMODYNAMICS (THER 205)

 

TUTORIAL EXAMPLES : APPLICATIONS OF ENTROPY

 

 

1.         Draw a graph of Carnot Efficiency vs Heat input temperature (T1 ) for a heat rejection temperature of  30ºC.  (Use T1 = 100ºC - 2000ºC). From your knowledge of material properties - what is an approximate upper limited on hcarnot ? [soln]

 

2.         A Carnot engine receives heat at 140 ºC and rejects its heat via a cooling tower at 40ºC.  What percentage improvement  in efficiency is obtainable if it rejects its heat to sea-water at 8ºC? [+32%]

 

3.         Derive formulae to calculate the change in entropy of a perfect gas when it is:

                        (a)        heated at constant pressure from temperature T1   to T2  .

                        (b)        compressed at constant temperature from p1 to p2. [soln]

Use it to construct a T-s chart for air for pressures of 101.325 kPa and 1013.25 kPa.

 (Assume  s = 0  at p1 = 101.325 kPa and T1 = 273 K)

 

4.         A gas is throttled (suddenly reduced in pressure) from  900 kPa to 100 kPa.  No heat or work interactions occur and velocity and height changes are negligible.   What is             (a)        the final temperature?

                                                (b)        the change in specific entropy?

            If the gas is (A) Steam with x = 0.97,  (B) Air at 28 ºC.  [+0.955, +0.631 kJ/kgK]

 

5.         A cyclic process using a perfect gas is described by the following table:

Process

Heat transfer           

Work transfer           

DU

DS

Isothermal  1®2

a

2.485 kJ

b

c

Isobaric      2®3

d

e

f

g

Adiabatic    3®1

h

i

j

k

Summations     

l

m

n

p

 

Calculate the missing quantities a-p assuming each process is reversible. 
(Sketch the cycle on a p-V diagram and calculate p2 , V2 , V3)

            Given:               V1    =   0.01 m3 ,                T1   =   289 K

                                    p1   =    100 kPa,                  g  =   1.4

                                    [soln(a)], [soln(b)]

 

6.         Air expands from a pressure of 2 MPa to 30 kPa.  Calculate the specific work done if the air is at 1100 K, and the expansion is isentropic.  [-776.4 kJ/kg]

 

7.         Air is compressed in a water-cooled compressor from 110 kPa and 15 ºC to

850 kPa and 175 ºC. Calculate the polytropic index of compression (n), and the specific entropy change.    [n=1.275, -0.142 kJ/kgK]

                                                           

8.         Air at 200 kPa and 425 ºC is expanded through an adiabatic nozzle with an estimated isentropic efficiency of 0.93.  If the exit pressure is 80 kPa calculate the exit velocity.  (Assume the inlet velocity is negligible).   [550 m/s]