Question

A steam engine has a boiler that operates at 570 K. The energy from the burning fuel changes water to steam, and this steam then drives a piston. The cold reservoir's temperature is that of the outside air, approximately 300 K.

a. What is the maximum thermal efficiency of this steam engine?
b. If the 3500J of energy is supplied from the boiler, find the energy transferred to the cold reservoir and the work done by the engine on its environment.

Answer 1

ε = 47 %

W = 1645 J

Qc = 1855 J

Step-by-step explanation:

(a) The maximum thermal efficiency of an engine operating between two temperatures, Th and Tc ( hot and cold) is given by:

ε = 1 - Tc/Th

Substituting the values for our question:

ε = 1 - 300K/570K = 47 %

(b) The maximum efficiency just calculated relates to the work and heat as:

ε = W/Qh

where W is work, and Qh is the heat of the hot reservoir which is our energy input and W is the work extracted.

ε = W/Qh ⇒ W = ε x Qh = 0.47 x 3500 J = 1645 J

The energy transferred to the cold reservoir is givern by:

Qh - Qc = W ⇒ Qc = Qh - W = 3500 J - 1645 J = 1855 J