Question

Find out the work done in the following process.

• A. 61.5 Joule
• B. -61.5 Joule
• C. +246 Joule
• D. -246 Joule

Answer 1

The Correct Option is A

The problem requires finding the work done during the cyclic process shown in the PV diagram below.

The work done in a cyclic process is equal to the area enclosed by the path on the PV diagram.

Let's calculate the area:

1. The shape formed seems to be roughly elliptical, simplifying the area calculation.
2. The formula for the area of an ellipse is A = \pi \cdot a \cdot b, where a is the semi-major axis, and b is the semi-minor axis.
3. From the diagram, the pressure axis (P) runs from approximately 60 kPa to 340 kPa, giving a total length of 280 \, \text{kPa} and a semi-major axis a = 140 \, \text{kPa}.
4. The volume axis (V) runs from 60 cm³ to 320 cm³, giving a total length of 260 \, \text{cm}^3 and a semi-minor axis b = 130 \, \text{cm}^3.
5. Substitute these values into the ellipse area formula:

A = \pi \cdot 140 \, \text{kPa} \cdot 130 \, \text{cm}^3

Since 1 kPa = 1000 Pa and 1 cm³ = 10^-6 m³, the unit conversion gives:

A = \pi \cdot 140 \times 10^3 \, \text{Pa} \cdot 130 \times 10^{-6} \, \text{m}^3

Simplifying:

A = \pi \cdot 140 \cdot 130 \times 10^{-3} \, \text{J}

Calculating the numerical value:

A \approx \pi \times 140 \times 130 \times 10^{-3} \approx 61.5 \, \text{J}

Therefore, the work done is 61.5 Joule.

The correct answer is 61.5 Joule, which matches the given correct option.