Question

A vapour absorption refrigeration system is a heat pump with three thermal reservoirs as shown in the figure. A refrigeration effect of 100 W is required at 250 K when the heat source available is at 400 K. Heat rejection occurs at 300 K. The minimum value of heat required (in W) is

• A. 167
• B. 100
• C. 80
• D. 20

Answer 1

The correct option is C 80

Method I:

Given data:

$T_1=300K;T_2=250K;T_3=400K$

Refrigerating effect,
$Q_2=100W$



$COP=\left(\frac{T_2}{T_1-T_2}\right)\left(\frac{T_3-T_1}{T_3}\right)$

$=\left(\frac{250}{300-250}\right)\left(\frac{400-300}{400}\right)$

= 1.25

also $COP=\frac{Q_2}{Q_3}$

$\therefore 1.25=\frac{100}{Q_3}$

or $Q_3=\frac{100}{1.25}=80W$

Method II:

Using Clausius inequality;

$\oint \frac{\delta Q}{T}\le 0$

For the minimum value of heat required, the system must be reversible, i.e.

$\oint \frac{\delta Q}{T}=0$

$\therefore \frac{Q_2}{250}+\frac{Q_3}{400}=\frac{Q_1}{300}...\left(i\right)$

Also, $Q_3+Q_2=Q_1...\left(ii\right)$

From equation (i) and (ii)
After solving;

$Q_3=80Wand{Q}_1=180W$