Question

A cyclic process in a P-V diagram represents an ellipse as shown in fig. The network done is _______ kJ

• A. $13.62,\text{kJ}$
• B. $23.562,\text{kJ}$
• C. $27.562,\text{kJ}$
• D. $63.2,\text{kJ}$

Answer 1

The correct option is B $23.562,\text{kJ}$

Given: $P_C=75kPa;P_D=25kPa:V_A=0.2m^3;V_B=0.8m^3$

We know that area under the PV curve gives the work transfer.

So, Area of ellipse = Net work transfer

$Areaofellipse=\pi$ab

Where, a = length of semi major axis

b = length of semi minor axis

$\therefore$ $a=\frac{V_B-V_A}{2}=\frac{0.8-0.2}{2}=0.3$

$Andb=\frac{P_C-P_D}{2}=\frac{75-25}{2}=25$

$Now,Networktransfer=\pi$ab

$W_{net}=\pi \times 0.3\times 25$

$=23.562kJ$