Question

Steam locomotives have an efficiency of 18.0% and operate with a hot steam temperature of 425°C.

(a) What would the cold reservoir temperature (in °C) be if this were a Carnot engine? °C

(b) What would the maximum efficiency of this steam engine be if its cold reservoir temperature were 150°C? %

Answer 1

Part (a)

Temperature of the hot steam = T_h = 425 ^oC = 425 + 273 K = 698 K

Temperature of the cold reservoir = T_c

Efficiency of the steam locomotive = = 18% = 0.18

The steam locomotive is considered as a carnot engine therefore,

T_c = 572 K

T_c = 572 - 273 ^oC

T_c = 299 ^oC

Part (b)

Temperature of the hot steam = T_h = 425 ^oC = 425 + 273 K = 698 K

Temperature of the cold reservoir = T_c = 150 ^oC = 150 + 273 K = 423 K

Maximum efficiency of the steam locomotive = _max

Maximum efficiency is equal to the carnot efficiency.

_max = 0.394

_max = 39.4%

a) Cold reservoir temperature if the steam locomotive were a carnot engine = 299 ^oC

b) Maximum efficiency of the steam engine if it's cold reservoir temperature were 150 ^oC = 39.4%