Question

A Carnot engine operates with an efficiency of 26.0% when the temperature of its cold reservoir is 281 K. Assuming that the temperature of the hot reservoir remains the same, what must be the temperature of the cold reservoir in order to increase the efficiency to 35.0%?

Answer 1

The temperature of cold reservoir should be 246.818 K for efficiency of 35%

Step-by-step explanation:

In first case we have given efficiency of Carnot engine = 26 % = 0.26

Temperature of cold reservoir
`T_L=281K`

We know that efficiency of Carnot engine is given by

`\eta =1-(T_L)/(T_H)`

`0.26 =1-(281)/(T_H)`

`T_H=379.72K`

For second Carnot engine efficiency is given as 35% = 0.35

And temperature of hot reservoir is same so
`T_H=379.72K`

So
`0.35=1-(T_L)/(379.72)`

`T_L=246.818K`

So the temperature of cold reservoir should be 246.818 K for efficiency of 35%