Question

An engine manufacturer makes the following claims: An engine’s heat input per second is 9.0 kJ at 435 K. The heat output per second is 4.0 kJ at 285 K.

a) Find the theoretical maximum possible efficiency for this engine.

b) Do you believe these claims?

Answer 1

Solution:- Given- Q1 = 9.0 KJ , Q2 = 4 KJ and T1 = 435K, T2 = 285K

Efficiency, e = 1 - Q2/Q1

=> e = 1 - (4/9)

=> e = 1 - 0.44

=> e (theoretical)= 0.555 = 0.56.

Thus, the theoretical maximum efficiency of this engine would be 0.56.

Now, efficiency for ideal gas case will be equal to 1 - (T2/T1)

=> e(ideal) = 1 - (T2/T1)

Now,

Putting the values of T1 and T2

=> e(ideal) = 1 - (285/435)

=> e(ideal) = 1 - 0.655

=> e(ideal) = 0.34

Now, on comparing e(theoretical) and e(ideal), we find that e(theoretical) = 0.56 which is more than e(ideal) which is 0.34 and this is not practically possible. Hence, the claim is not correct.