Saturday, June 30, 2007

MCQ on Carnot Engine

A brief discussion on heat engine and refrigerator was made in the post dated 20th February, 2007 in which you will find a few typical multiple choice questions. You can find the post by clicking on the label ‘Carnot engine’ or ‘thermodynamics’ below this post or on the side of this page.

Here is another MCQ on Carnot engine (reversible heat engine):

A Carnot engine converts 1/5th of the heat, which it absorbs from the source, into work. When the temperature of the sink is reduced by 100º C, its efficiency is doubled. The temperature of the source is

(a) 400 K (b) 450 K (c) 500 K (d) 600 K (e) 700 K

If T1 and T2 are the temperatures of the source and sink respectively, the efficiency (η) is given by η = (T1 – T2)/T1.

Therefore, initially we have 1/5 = (T1 – T2)/T1 so that T2 = 4T1/5.

In the second case (when the temperature of the sink is reduced), we have

2/5 = [T1 – (T2 – 100)]/T1.

Substituting for T2 (= 4T1/5) in the above equation, we obtain T1 = 500 K.