Question

A carnot engine has the same efficiency between 100k and 500k as between T k and 1000k. T being the lower temperature, find T.

Answer 1

Answer:

Let efficiency of the Carnot's engine be denoted be "n"

You should remember the formula for efficiency i.e [n = 1- T2/T1],

where T2 is the temperature of the sink (lower temperature) and T1 is the temperature of the source (higher temperature).

Now as per the question, the efficiency of the engine is same in the given temperature ranges

therefore,

n1 =n2

=> 1- 100/500 = 1- T/1000

=> 1/5 = T/1000

=> T = 200 K

The answer is T = 200 K