Question

A Carnot engine has an efficiency of 0.537, and the temperature of its cold reservoir is 379 K.

(a) Determine the temperature of its hot reservoir.
(b) If 6580 J of heat is rejected to the cold reservoir, what amount of heat is put into the engine?

Answer 1

(A) Th = 818.6 K

(B) Qh = 14211.7 J

Step-by-step explanation:

efficiency (n) = 0.537

temperature of cold reservoir (Tc) = 379 K

heat rejected (Qc) = 6580 J

(A) find the temperature of the hot reservoir (Th)

n = 1 -
`(Tc)/(Th)`

0.537 = 1 -
`(379)/(Th)`

`(379)/(Th)` = 1 - 0.537 = 0.463

Th =
`(379)/(0.463)`

Th = 818.6 K

(B) what amount of heat is put into the engine (Qh) ?

from
`(Tc)/(Th) = (Qc)/(Qh)`

Qh = 6580 ÷
`(379)/(818.6)`

Qh = 14211.7 J