Question

A gas turbins has T_H = 1600K and T_C=800K. Hot exhaust from the gas turbine is used to run a steam turbine with T_H=800K, T_C=300K. Calculate:

a) the maximum efficiency of the gas turbine

b) the maximum efficiency of the steam turbine

c) the maximum combined efficiency of the gas and steam turbines operating together

d) the maximum work done on the surroundings for every 1.00MJ heat absorbed at 1600K. Hint: q_H for the steam turbine = -q_C for the gas turbine.

Answer 1

this question is based on the second law of thermodynamics

a) the maximum efficiency is given by

hence it is (1600-800)/1600 = 0.5 or 50%

b) it is (800-300)/800 = 0.625 or 62.5%

c) the combined efficiency of two carnot engines kept in series will depend only on the reservoir and the final sink in which the energy is drained, which in our case will be Th=1600K and Tc=300K

hence efficiency = (1600-300)/1600 = 13/16 = 0.8125 or 81.25%

d) q2 - heat absorbed by gas turbine ; q1 - heat given out by gas turbine

q4 - heat absorbed by steam turbine ; q3 - heat given out by steam turbine

q1 = -q4

thus

q2 = +1000000 J, T2 = 1600K, T1 = 800K

hence q1= -500000J = -q4

hence q4 = 500000J

T4 = 800K, T3 = 300K

hence q3 = -187500J

total work done by the two engines = -(q2+q1) - (q4+q3)

W = -(1000000-500000)-(500000-187500)

=-812500J is the required total work done.